Dustin Smith (2015) claims that several passages in John, like John 8:58 and 17:5, are actually referring to figurative pre-existence in the mind of God rather than saying that Jesus literally pre-existed his birth. He cites passages from Jewish and Christian literature to show that things were thought of as existing before their creation:

• “Have you not heard? Long ago I did it, from ancient times I planned it. Now I have brought it to pass.” (2 Kings 19:25)
• “From the God of knowledge stems all there is and all there shall be. Before they existed he made all their plans and when they came into being they will execute all their works in compliance with his instructions, according to his glorious design without altering anything.” (1QS 3:15-16)
• “inherit the kingdom prepared from the foundation of the world” (Matthew 25:34)
• “Worthy are You, our Lord and our God, to receive glory and honor and power; for You created all things, and because of Your will, they were, and were created.” (Revelation 4:11)
• “Seven things were created before the world was made, and these are they: Torah, repentance, the Garden of Eden, Gehenna, the throne of glory, the house of the sanctuary, and the name of the Messiah.” (Pesachim 54a:8)
• “Six things preceded the creation of the world; some of them were created and some of them were decided to be created. The Torah and the Throne of Glory were created… The Patriarchs, Israel, the Temple, and the name of the Messiah were decided to be created.” (Genesis Rabbah 1:4)

That this was commonly applied to people, not just things:

• “Before I formed you in the womb I knew you, and before you were born I sanctified you and ordained you a prophet to the nations.” (Jeremiah 1:5)
• “Abraham and Isaac were created before any work.” (Prayer of Joseph 1:2)
• “For this is what the Lord of the world has decreed… He did design and devise me [Moses], who (was) prepared from the beginning of the world, to be mediator of His covenant. Therefore, I shall speak plainly to you.” (Testament of Moses 1:14)
• “number her among your people that you have chosen before all things came into being” (Joseph and Aseneth 8:9)

That this was applied specifically to the Messiah:

• “God will reveal His Messiah whose name is spoken from the beginning” (Targum Zechariah 4:20)
• “the Messiah, who was indeed foreknown before the foundation of the world, but manifested in the last times for your sake” (1 Peter 1:20)
• “names written in the scroll of the lamb, who was slaughtered from the foundation of the world” (Revelation 13:8)
• “Seven things were created before the world was made… the name of the Messiah.” (Pesachim 54a:8)
• “Six things preceded the creation of the world… the name of the Messiah [was] decided to be created.” (Genesis Rabbah 1:4)

That things pre-existing in the mind of God could be said to be “with God”:

• “And the Lord said to me: “This city will be delivered up for a time…Or do you think that this is the city of which I said, ‘On the palms of My hands I have carved you?’ It is not this building that is in your midst now; it is that which will be revealed, with Me, that was already prepared from the moment I decided to create Paradise. And I showed it to Adam before he sinned. But when he transgressed the commandment, it was taken away from him—as also Paradise. After these things I showed it to My servant Abraham…And I showed it also to Moses on Mount Sinai…Behold, now it is preserved with Me—as also Paradise.” (2 Baruch 4:1-6)
• “R. Huna said in the name of R. Eliezer, the son of R. Jose the Galilean: “Even those whereof it is written, ‘For, behold I created new heavens’ (Isa. 65:17), have been created long ago, since the six days of Creation, as it is written, ‘For as the new heavens…remain before Me’ (Isa. 66:22): not ‘new’ is written here, but ‘the new.’“” (Genesis Rabbah 1:13)

Greek 📜
The translation in Greek text is a proper sentence, called a PPA (Present of Past Action).
So taking εἰμι in John 8:58 as a present of past action or extension from the past is a minority position among some scholars. Kenneth L. McKay’s A New Syntax of the Verb in New Testament Greek (Peter Lang, 1994) says that εἰμι in 8:58 is “a form of the continuation realization of the imperfective aspect” and renders the verse as “I have been in existence before Abraham was born” (p. 42). Jason BeDuhn has also argued for this reading. The majority position however understands ἐγώ εἰμι in the verse not merely in terms of tense/aspect but in light of the use of this expression contextually in John and in the OT, as the equivalent of Hebrew אני הוא as solemn divine pronouncement, particularly in Deuteronomy 32:39 and in Deutero-Isaiah (Isaiah 41:4, 43:10, 13, 25, 44:6, 46:4, 48:12). On this see especially Catrin H. Williams’ I Am He: The Interpretation of ‘Anî Hû in Jewish and Early Christian Literature (Mohr Siebeck, 2000). This explanation is much more satisfying because it accounts for the absolute use of ἐγώ εἰμι elsewhere in the same discourse in John 8:24, 28 as well as in 13:19, which is clearly dependent on these passages from Deutero-Isaiah (ἵνα γνῶτε καὶ πιστεύσητε καὶ συνῆτε ὅτι ἐγώ εἰμι in Isaiah 43:10 LXX; cf. πιστεύσητε ὅτι ἐγώ εἰμι in John 8:24, γνώσεσθε ὅτι ἐγώ εἰμι in 8:28, and ἵνα πιστεύσητε ὅτι ἐγώ εἰμι in 13:19), with Jesus appropriating these divine pronouncements. The present tense in 8:58 thus appears to be a timeless present drawing on Deutero-Isaiah’s emphasis of God’s eternity (e.g. ἐγώ εἰμι πρῶτος καὶ ἐγώ εἰμι εἰς τὸν αἰῶνα in Isaiah 48:12 LXX). There is a possible parallel in Isaiah 43:13 MT (גם מיום אני הוא, “before the day [existed], I am [he]”), which is difficult but understood in the LXX, Vulgate, Targum as referring to creation (e.g. ἔτι ἀπ’ ἀρχῆς in the LXX although the text that follows is defective without a parallel to אני הוא except in Lucianic revision). Another timeless present occurs in Psalm 90:2 (LXX 89:2): πρὸ τοῦ ὄρη γενηθῆναι καὶ πλασθῆναι τὴν γῆν καὶ τὴν οἰκουμένην καὶ ἀπὸ τοῦ αἰῶνος ἕως τοῦ αἰῶνος σὺ εἶ “Before mountains were brought forth and the earth and the world were formed, and from everlasting to everlasting, you are”. Williams notes in connection with 8:58:
“To interpret έγώ είμι exclusively in terms of timeless divine existence does not, however, convey the full force of the expression in 8:58. If אני הוא is the ultimate ‘source’ of this Johannine pronouncement, the inextricable link between God’s eternal presence and his salvific activity must also be taken into account. Deutero-Isaiah pronounces that God is both ‘first’ and ‘last’ because his creative and salvific acts extend from beginning to end. Similarly, έγώ είμι of John 8:58 is not only concerned with establishing Jesus’ pre-existence or his precedence over Abraham, but it serves as the basis for his overall promise of salvation. Thus, as effectively noted by Lindars, if the Johannine Jesus is to be presented as the giver of eternal life, it must be shown that he himself possesses a life with no such limitations as a beginning and an end (1:4; 5:26; 6:57; 14:19)….Abraham is thus depicted as a witness to the revelation of divine salvation in Jesus (v. 56: και είδεν και έχάρη). In the poetry of Deutero-Isaiah, the patriarch is presented as one who has already experienced God’s power to deliver (Isa. 51:2; cf. 41:8), and this offers assurance to the exiles of their own future deliverance…Once again, to recognize הוא in its role as a distinctive designation for God would clearly be dependent on the setting of its usage. If Jesus, according to John 8:58, was accused of blasphemy for usurping the divine הוא , it would have to be clear from the context of his pronouncement that this was its intended function…Jesus has, moreover, been making pronouncements throughout the discourse that would be viewed as claims to divine authority by his opponents, and to speak of himself in relation to the patriarch Abraham with the words πριν ‘Αβραάμ γενέσθαι could quite plausibly have prompted his Jewish audience to interpret אני הוא as his claim to a divine name” (pp. 277-282).
BeDuhn uses the term “gibberish” to characterize the common rendering of John 8:58 (“Before Abraham was born, I am”). For example consider the very similar Psalm 90:2(89:2) LXX which conveys the same thought. Brenton’s translation renders it as: “Before the mountains existed, and before the earth and the world were formed, even from age to age, Thou art.” The recent NETS translation (which I quoted in my above post) similarly has: “Before mountains were brought forth and the earth and the world were formed, and from everlasting to everlasting, you are”. This doesn’t read as ungrammatical to me and rather poetically conveys the idea that God transcends time and space. The only difference between this and John 8:58 is that the latter is in first person rather than second person.
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More of an exegesis of John 8.58 📜
The use of the present tense here expresses the thought that for God, all time to him is present tense (an eternal or timeless present tense). John 1:1 already said that the Logos (incarnated as the man Jesus) existed before creation with God and has his divine nature (θεὸς ἦν ὁ λόγος). The closest parallel to John 8:58 in the OT (as mentioned in George R. Beasley-Murray’s WBC volume, p. 139) is Psalm 90:2(89:2) LXX which conveys the same thought but in the second person rather than first: πρὸ τοῦ ὄρη γενηθῆναι καὶ πλασθῆναι τὴν γῆν καὶ τὴν οἰκουμένην καὶ ἀπὸ τοῦ αἰῶνος ἕως τοῦ αἰῶνος σὺ εἶ. Brenton’s translation renders it as: “Before the mountains existed, and before the earth and the world were formed, even from age to age, Thou art.” The recent NETS translation similarly has: “Before mountains were brought forth and the earth and the world were formed, and from everlasting to everlasting, you are”. The use of the present tense here is not odd but poetically conveys the idea that God transcends time and space. Psalm 90:4 continues this idea: “A thousand years in your sight are like a day that has just gone by, or like a watch in the night”.
So just on this basis Jesus is claiming a timelessness that otherwise belongs to God. But there are echoes here of the divine use of אני הוא in the OT. This is the third of a series of pronouncements utilizing an absolute ἐγώ εἰμι (without a predicate noun), the prior two being allusive of the divine use of אני הוא in Isaiah 43:10 LXX (John 8:24, 28; cf. also 13:19). On this see especially Catrin H. Williams’ I Am He: The Interpretation of ‘Anî Hû in Jewish and Early Christian Literature (Mohr Siebeck, 2000). So this explanation accounts for the absolute use of ἐγώ εἰμι elsewhere in the same discourse in John 8:24, 28 as well as in 13:19, which is clearly dependent on these passages from Deutero-Isaiah (ἵνα γνῶτε καὶ πιστεύσητε καὶ συνῆτε ὅτι ἐγώ εἰμι in Isaiah 43:10 LXX; cf. πιστεύσητε ὅτι ἐγώ εἰμι in John 8:24, γνώσεσθε ὅτι ἐγώ εἰμι in 8:28, and ἵνα πιστεύσητε ὅτι ἐγώ εἰμι in 13:19), with Jesus appropriating these divine pronouncements. The present tense in 8:58 thus appears to be a timeless present drawing on Deutero-Isaiah’s emphasis of God’s eternity (e.g. ἐγώ εἰμι πρῶτος καὶ ἐγώ εἰμι εἰς τὸν αἰῶνα in Isaiah 48:12 LXX). There is a possible parallel in Isaiah 43:13 MT just a few verses away from 43:10 (גם מיום אני הוא, “before the day [existed], I am [he]”), which is difficult but understood in the LXX, Vulgate, Targum as referring to creation (e.g. ἔτι ἀπ’ ἀρχῆς in the LXX although the text that follows is defective without a parallel to אני הוא except in Lucianic revision). These declarations in Deutero-Isaiah are the clearest expression of monotheism in the OT so it is striking that Jesus is speaking with the same voice. Note also Isaiah 47:8, 10 in which evildoers facing divine punishment usurp and imitate God’s use of ἐγώ εἰμι from 45:18. Williams writes in the above-mentioned book:
“To interpret έγώ είμι exclusively in terms of timeless divine existence does not, however, convey the full force of the expression in 8:58. If אני הוא is the ultimate ‘source’ of this Johannine pronouncement, the inextricable link between God’s eternal presence and his salvific activity must also be taken into account. Deutero-Isaiah pronounces that God is both ‘first’ and ‘last’ because his creative and salvific acts extend from beginning to end. Similarly, έγώ είμι of John 8:58 is not only concerned with establishing Jesus’ pre-existence or his precedence over Abraham, but it serves as the basis for his overall promise of salvation. Thus, as effectively noted by Lindars, if the Johannine Jesus is to be presented as the giver of eternal life, it must be shown that he himself possesses a life with no such limitations as a beginning and an end (1:4; 5:26; 6:57; 14:19)….Abraham is thus depicted as a witness to the revelation of divine salvation in Jesus (v. 56: και είδεν και έχάρη). In the poetry of Deutero-Isaiah, the patriarch is presented as one who has already experienced God’s power to deliver (Isa. 51:2; cf. 41:8), and this offers assurance to the exiles of their own future deliverance…Once again, to recognize הוא in its role as a distinctive designation for God would clearly be dependent on the setting of its usage. If Jesus, according to John 8:58, was accused of blasphemy for usurping the divine הוא , it would have to be clear from the context of his pronouncement that this was its intended function…Jesus has, moreover, been making pronouncements throughout the discourse that would be viewed as claims to divine authority by his opponents, and to speak of himself in relation to the patriarch Abraham with the words πριν ‘Αβραάμ γενέσθαι could quite plausibly have prompted his Jewish audience to interpret אני הוא as his claim to a divine name” (pp. 277-282).
This then raises the question of God’s pronouncements in Exodus where he revealed his name Yahweh to Moses. J. Ramsey Michaels in his NICNT commentary notes that the LXX occasionally renders אני itself as a divine name in Deutero-Isaiah, producing the expression “I am the ‘I am’ ” or even אני יהוה as “I am the ‘I am”, the Lord” (see ἐγώ εἰμι ἐγώ εἰμι in Isaiah 43:25 LXX which again is in the same passage as 43:10, ἐγώ εἰμι ἐγώ εἰμι κύριος in 45:19 LXX). This doubled “I am” expression is somewhat reminiscent of Exodus 3:14: ἐγώ εἰμι ὁ ὤν in the OG and ἔσομαι (ὃς) ἔσομαι (“I will be what I will be”) in Theodotion and Aquila, but it uses ἐγώ εἰμι itself as the predicate rather than ὁ ὤν (which itself became a divine epithet in Philo of Alexandria and for the author of Revelation). The other echo is in Exodus 3:6 (which is cited in the synoptic tradition, see Mark 12:27 and parallels). God reveals himself saying ἐγώ εἰμι ὁ θεὸς τοῦ πατρός σου θεὸς Αβρααμ καὶ θεὸς Ισαακ καὶ θεὸς Ιακωβ. When Jesus says πρὶν Ἀβραὰμ γενέσθαι ἐγὼ εἰμί, the catchword connection with Αβρααμ could suggest to a hearer that Jesus was about to say ἐγώ εἰμι ὁ θεὸς τοῦ πατρός σου θεὸς Αβρααμ but he stops short, with an absolute ἐγὼ εἰμί instead evoking God’s pronouncements in Deuteronomy (see for instance 32:29) and Deutero-Isaiah. Relevant here also is the claim in Philo of Alexandria that it was the Logos who was speaking to Moses at the burning bush (De Confusione Linguarum 146, De Migratione Abrahami 14, De Vita Mosis 1.66, etc.), with the use of ὁ λόγος in John likely drawing from Philo.

The more direct connection isn’t with Ex 3:14, but with Isaiah 34:10 which occurs in a context that 2nd Temple Jews used as a proof-text for monotheism.

“πιστεύσητε ὅτι ἐγώ εἰμι” (John 8:24)

“πιστεύσητε … ὅτι ἐγώ εἰμι” (Isa 34:10), where still it is YHWH speaking.

For more examples of how early Christians made this sort of move, see: Bauckham, Richard. Jesus and the God of Israel: God Crucified and Other Studies on the New Testament’s Christology of Divine Identity. Grand Rapids, MI: Eerdmans, 2008.