Almost everything I "know" about Jews in Egypt comes from Jewish or Christian teachings. I'm curious if there are any records from Egypt that corroborate the Jewish stories of Egypt (particularly that of Moses, but preliminary searches indicate that such records don't appear to exist).
It's probably waaaay too late for your interests, but we do have at least one very substantial collection of Achaemenid era papyri and ostraca dealing with a Jewish community on Elephantine Island. These papyri mostly document the day-to-day life on the Island, with the Jews mostly connected to the Persian military garrison. This incidentally makes them an extremely important source not just for Jewish history but for Achaemenid Persian history because they provide one of the relatively few collections of administrative documents from the Empire. This archive provides the oldest known documentation of Passover(the so-called "Passover Letter") as well as a series of documents concerning the Temple of YVWH built on the island and the conflict in which temple was leveled, possibly on the instigation of the priests of Khnum.