There’s no archeological/historical evidences supporting the exodus account. No mention of Moses, no mention of numerous Hebrews building towns, no mention of the plagues, no mention of the drowning of an army, etc…Beside, the number of Hebrws fleeing Egypt mentionned in the bible is totally unbelievable : it would be the equivalent of the whole estimated population living in the Nile delta at his time.
Of course, it doesn’t mean that there couldn’t have been some Hebrews living in Egypt, being enslaved or something equivalent, etc… There aren’t records for every little thing that could have happened in Egypt.
Assuming that the bible story is based on some true original event (which could be possible…or even likely, since the account survived until today and was considered by the Hebrews as a major, and even founding, event), my take would be that some little group of Hebrews who were unhappy with something in Egypt fled this country in some heroic or noticeable way and that the tale was told from generation to generation in the tribe founded by the original heroes, or to which they belonged, was way exagerated and considered as a founding event, spread amongst the other Hebrew tribes when they began to unify and eventually was recorded in the Bible much later.
Now, as for the Hebrews and Egypt (the little I know about it) :
-In the area around Egypt lived various nomadic tribes, which were at time very annoying, or at other times could at the contrary would prove useful. The Hebrews are likely to have been in close contact with Egypt which was by far the single most powerful nation in the area. There certainly was at various times people from these tribes settling in Egypt, or fighting for the Egyptians, or working for them (and of course occasionnally raiding them).
-There are mentions of nomads coming from the east of Egypt who were allowed in time of drought to come in the border areas of the country in order for their herds to drink/graze. Once again the Hebrews could have been amongst them.
-There’s a single mention of a people called “Habiru” living I can’t exactly remember where, but roughly in the southern part of what is now Israel, IIRC. It’s generally assumed that it refers to the Hebrews and that is the very first mention of them in recorded history. So, at some point, the Egyptians knew there were such a people living around and had contact with them.
-In much latter times (much latter by comparison with the usual dates given for the Exodus), there are records of the presence of the Hebrews in Egyptia, in particular serving as soldiers/mercenaries. For instance Hebraic people garrisoned in Egypt asked the temple in Jerusalem whether they could build a shrine and worship there (incidentally, they asked also questions about how they should worship some other deities than YHWH, which prove the Hebrew weren’t that monotheistic at this time)
