The Gathas in Old Avestan are generally dated to the late second millennium BCE. P. Oktor Skjaervø (in The Indo-Aryans of Ancient South Asia: Language, Material Culture, and Ethnicity, pp. 166-167; De Gruyter, 1995) dates Old Avestan to the 14th to 11th centuries BCE, or possibly even earlier (such as the 15th century BCE). Almut Hintze gives a date of c. 1200 BCE for Zarathustra and the Old Avestan liturgies (see his paper in The Literature of Pre-Islamic Iran; Bloomsbury, 2009). Michiel de Vaan in The Avestan Vowels (Rodopi, 2003) argues that the Old Avestan texts were orally composed 1200-1000 BCE and canonized a few centuries later. The reception of the Gathas in the Achaemenid period is clear from both nomenclature and inscriptions (on the former see the work of Avestan scholar Jean Kellens). So this material is assuredly older than Hebrew biblical texts and comparison with OT literature has been fruitful; on the relationship between Y. 31, 44 and Deutero-Isaiah, see Joseph Blenkinsopp’s “The Cosmological and Protological Language of Deutero-lsaiah”, CBQ 2011 and Tina D. Nilsen’s “Creation in Collision? Isaiah 40-48 and Zoroastrianism, Babylonian Religion and Genesis 1”, JHS 2013.
The next chronological layer are the Young Avestan texts which were orally composed in c. 900-400 according to Skjaervø and c. 800-300 BCE according to de Vaan. This is a language roughly contemporary with Old Persian and while Young Avestan compositions largely antedated the Achaemenids, they originated in eastern Iran and Pakistan around Sistan and did not influence the Persian west until the later period. Their Persian reception is attested by the residue of Old Persian pronunciations in the received text (the transition to Middle Persian occurred around 300 BCE as inscriptions show) as shown by Karl Hoffmann, as well as allusion and paraphrase of Young Avestan ideas in Xerxes’ Daiva inscription (as discussed by Skjaervø) and in Greek works from the late Achaemenid period by Eudemus of Rhodes and Theopompus, which were reported on by later writers. Plutarch, dependent on Theopompus, even gives a verbatim paraphrase of Yt. 8.44, indicating that some of the Avestan liturgies were translated into Greek (on the reception of the Avesta in Greek sources see Albert de Jong’s Traditions of the Magi: Zoroastrianism in Greek and Latin Literature; Brill, 1997). The latest portions of the Avesta are roughly contemporary with the composition of OT post-exilic works, whose influence may have been felt particularly in the subsequent Hellenistic period. This is also a fruitful area for studying potential Zoroastrian influence. Yishai Kiel (VT, 2013) has pointed to similarities between the Holiness Code and Vidēvdād and Almut Hintze’s “Defeating Death: Eschatology in Zoroastrianism, Judaism, and Christianity” (in Irano-Judaica VII: Studies Relating to Jewish Contacts With Persian Culture Throughout the Ages; Ben-Zvi, 2019) examines the relationship between the concept of resurrection in the Young Avesta and Jewish apocalyptic texts.
The next chronological layer dating to the Seleucid and Arsacid periods. When the Young Avestan language was dying out, expository works on Avestan liturgies were composed in Middle Persian which reveal an inaccurate understanding of the language. Fragments Westergaard is from an earlier expository work composed in Young Avestan that survived the period. But all these other works were written down in Pahlavi in the Sasanian and Islamic periods so it is difficult to distinguish between early material and later redactions and compositions. There is philological evidence for an Avestan vorlage for Bahman Yašt (Zand-i Wahman Yasn), or rather the lost work it is a commentary of (see for instance Dan Shapira’s 2013 article in Journal of Persianate Studies), and Bundahišn likely contains some early material along with compositions dating many centuries later. These are the two writings that offer many promising parallels to Jewish and Christian eschatology and their use has to be judicious since they may contain Christian influence (with Syriac Christian evangelism in Mesopotamia and Iran in the second and third centuries CE). For a good example of the latter, see Vincente Dobroruka’s recent Persian Influence on Daniel and Jewish Apocalyptic Literature (Bloomsbury, 2022). There were also Zoroastrian works composed in Greek during this period, particularly in Asia Minor which contained a thriving Zoroastrian community before the rise of Christianity. Foremost among the Zoroastrian pseudepigrapha is the Oracles of Hystaspes (likely dating to the first century BCE) which became popular among Christians and which may have influenced Revelation (as discussed by David Aune in his commentary).
The Dēnkard Avesta was a compendium of Pahlavi and Avestan texts largely of an expository nature, dating to the Islamic period with named authorship of some of the material to the 9th century CE. It certainly contains much earlier material but the composition itself is very, very late. Nask 6 is a collection of didactic material with no known date beyond the likely time of composition. The possibility of Greco-Roman, Christian, and Islamic influence is quite strong here.