What we'd expect if the exodus was real is either proto-semitic writings about the event or even Egyptian writings. Because, fun fact, slaves tend to speak the language of their masters. The fact that the only document we have about it is written in Ancient Hebrew, a language that first debuted around 900 BCE, puts a lot of this into question.
The exodus was supposed to have happened anywhere from 1400BCE to 1200BCE (the bible gives at least 2 dates).