That question of timing and influence will be debated forever. In many researchers' minds the Greeks (broadly speaking) are the beginning of the whole genre of the 'saga' and it must be said their reach and influence predates, by hundreds of years, the empire of Alexander through trade, mercenaries and migration...Philistines???
The general argument is that the increasing sophistication of Yahwist scribal theology motivated introjections into both rival their national saga (Primary History). The insertion of an angel or Word or Glory is rather clearly a secondary layer. The most likely period for this was the 4th-3rd century BCE IMO. Whether this is the direct result of Greek exposure (post Alexander) is speculative. Until recently I favored this idea, and many still do, but the underlying premise is that the Judeans (or Diaspora) were somehow primitive, less culturally advanced than the empires that repeatedly laid waste to them. That is just not supported by evidence. Wherever the Jews found themselves (Babylon, Peria, Egypt) they asserted an influence and found respect in intellectual circles.
Regarding the Logos terminology, that was the work of great Greek minds specifically. The record is pretty clear on that point. That does not mean other thinkers had not arrived at something somewhat similar. That is likely the case here. While the Alexandrian Jews especially, adopted the language of Neoplatonism, their message would have been familiar to a broader audience. Just how indebted the scribes that introduced the 'Angel of the Lord' (and Glory, or Word, or Name) were to the Greeks is impossible to quantify.