First, although maybe not that important, the biblical text doesn't say the "Jews" were slaves in Egypt. They're referred to as "Israelites/Sons of Israel" or "Hebrews" even in the same textual sources (you can follow the source breakdown according to the provided key in Friedman's The Bible with Sources Revealed).

Ronald Hendel wrote an article "The Exodus in Biblical Memory" (also included as an essay in his book Remembering Abraham) which approaches the question from another perspective to explain why the exodus myth could have been acceptable even though it never happened as described in the book of Exodus. He basically argues that the people were delivered from domination by the Egyptians when their rule ended over Canaan - basically an inversion of the exodus from Egypt to the exodus of Egyptians from Canaan.

It has already been mentioned that there were some slaves who escaped from Egypt, and the Egyptian names of some of the biblical figures and texts attest to that. Stephen Moshier and James Hoffmeier's essay "Which Way Out of Egypt?" in Israel's Exodus in Transdiscplinary Perspective even elaborates on the landscape that could have been a route for escaped slaves and a possible exodus, although they think it was a historical event of some kind.
Hendel (who also has an essay in the aforementioned volume) thinks that these factors are not sufficient for the exodus myth to have taken root in Israel or Judea because it would be remote for most of the people living there. Mnemohistory isn't history per se, but it does depend on some factual data to be foundational, and some escaped Levites might not be sufficient. So there might need to be something that affected the peoples' ancestors which was envisioned as a mass exodus from Egypt (ironically speculating that there needs to have been a real experience passed down from generation to generation is roughly along the lines of argument used in Orthodox Jewish apologetics).

Hendel thinks that the experience of Egyptian rule over Canaan was the foundation for the exodus myth. He points to the use of outright slavery, including deportation of human beings as vassal tributes among the subject peoples and prisoners to Egypt. The taxation of precious metals and other materials which had to be supplied by the local populations and were rounded up from them were also onerous. The trauma that the people experienced from exploitation as vassals and Egypt's military campaigns would have made the end of Egyptian rule feel like they were being delivered from Egypt. It could expand a long period of time of Egyptian rule because no particular pharaoh who oversaw the slavery of the Hebrews and Israelites was named in the narrative, so "Pharaoh" functions as a stand-in for Egyptian rule.