Would like to add to OP's question: BESIDES THE BIBLE/TALMUD, since that tends to be the only source people use to refer to the event.

From what I've gathered researching this independently there is absolutely no physical evidence of Jewish enslavement in Egypt besides the less than credible evidence from scripture. Because it is scripture there have been many attempts to try and demonstrate the exodus and Moses as historical fact.

However, there is great difficulty identifying which Pharoah ruled Egypt at the time of the Exodus, there are several candidates spanning a period of 500 years From Thutmose II, Akhentaten, Ramsses II, etc

Further, the numbers given by the Bible number the Jews at about 600,000 when Egypt itself numbered 2 million at the time. Assuming we have a clear idea of the time, and such a large number of people leaving at the same time would have been both impossible and catastrophic.

If you'd like to leave historicity for the realm of conspiracy one theory that I can't find the book for here at home suggests that Moses was an Egyptian priest and supporter of Pharaoh Akhentaten and led a few hundred followers out of Egypt after that Pharaoh's death and this could be the origin of monotheism in Judaism, but archaeological evidence in Israel could probably discredit that point of view.

As of yet I have come accross nothing resembling objective non biblical evidence of the existence of any significant number of Jews or Jewish slaves in Egypt.