It should be noted that the Aramaic documents found on Elephantine Island are connected to the Persian occupation of Egypt. To quote the Wikipedia
"Though some fragments on papyrus are much older, the largest number of papyri are written in Aramaic, the lingua franca of the Persian Empire, and document the Jewish community among soldiers stationed at Elephantine under Persian rule, 495–399 BCE"
Egypt came under Persian rule during the reign of Cambyses,starting around 530 BC and Darius I, who reigned until 486 BC, expanded the frontiers west into Libya and up the Nile river. Since the Persian garrison did not show up until after 500 BC, what Jewish community preceded them is a matter of conjecture..
I'd say that there is as much or more of a story in how the Persian Empire affected Judean beilefs versus the Egyptian influence.