In their Hermeneia commentary, Mark S. Smith and Elizabeth M. Bloch-Smith noted three things about this verse. First is that the phrase “Yahweh was with x” implies divine favor and so Judah enjoys full support from Yahweh in their conquest of the hill country. Also this is the only example of this construction with את in the book (instead עם occurs elsewhere in Judges, cf. 1:22, 2:18). Second, they note that כי may not be an adversative but a particle indicating the reason or evidence of the preceding assertion (as it is used later in the same verse). Third, they note that the verse has a late grammatical construction found in post-exilic and Qumran Hebrew (ל + לא-infintive) which means “it was not possible to”. So they translate the verse as follows: “Yahweh was with Judah and he took possession of the hill country, for it was not possible to dispossess the inhabitants of the plain, because they had chariots of iron”. This conveys quite a different meaning than the usual rendering. They also suggest that this verse may be a rather late redaction on the basis of the linguistic evidence.
The adversative implies that Judah had divine favor in taking the land in the plains but could not do so. The alternate reading makes Yahweh support Judah in taking the hill country (“the divine favor toward Judah pertains to the action that immediately follows”) and so they were successful. Indeed Judah is the only success mentioned here other than the Josephites’ conquest of Bethel in v. 22; all the other tribes fail in driving out the Canaanites from the land, and none of them are said to have Yahweh’s divine favor except for the tribes of Joseph in their successful conquest of Bethel (v. 21-27). The translation of the verbal construction also removes the necessary implication of a failed conquest. It was not possible to do Y so Judah did X, and they were victorious, thanks to Yahweh (cf. the same construction in 1 Chronicles 15:2 which does not imply that non-Levites tried to carry the ark but failed).
The verse under discussion here seems to be derivative of the story in Joshua 17 which concerned the tribes of Manasseh and Ephraim instead of Judah, who received an allotment in the hill country but wanted more land and were afraid of the military superiority of the Canaanites in the plains with their iron chariots. Their attitude contrasts sharply with the story of Caleb in ch. 14, suggesting that they lacked faith in Yahweh’s promise and wanted an extra allotment that avoided the problematic lowlands. Joshua promises that they will lay claim to these lands only after they put in the effort to overwhelm the Canaanites and drive them away. So it is more a matter of reluctance and cowardice than Yahweh failing to deliver for them. So the thought in Judges 1:19 may similarly be that the Judahites were intimidated of the powerful Canaanites in the plains and stopped short of attempting to drive them from the land.