Well, this is actually a very interesting question with quite a history behind it. As far as I am aware there is only a single inscription from ancient Egypt that even references the Hebrews and it loosely says (if I recall correctly) something like "the Hebrews lived over there". You would think that hundreds of thousands of people wandering in the desert for years would leave behind a trash heap, sandals, pottery...SOMETHING. But there is nothing that has been found.
But we also have to keep in mind that the absence of evidence is not evidence of absence. King David was thought for years to be a legendary figure akin to King Arthur until the discovery of the Tel Dan Stele in 1993. Granted there is still great disagreement among scholars about that but it does provide some evidence that David may have been a historical figure after all. The truth is that very few people from ancient history have a great deal of physical evidence to prove their existence. The only physical thing we have regarding Pontius Pilate, for example, is a dedication stone that loosely says "to Tiberius, with love, Pontius Pilate". It may be that physical evidence exists but has simply not been discovered by modern archaeologists. That is after all a big desert.
That being said, if there was a mass migration of Jews from Egypt it probably did not happen in the way the Exodus describes it for a variety of reasons. The main one is that prior to the Babylonian exile, Torah did not even exist in the form we see it today. It was only in post exilic Judea, for example, that Deuteronomy was added and the whole thing was highly redacted by the priests in order to maintain the identity of the Hebrews and give them something physical to hold on to. Off the top of my head I am not certain what (if anything) was changed specific to the actual story of the Exodus by the post-exilic priests (or so-called 'p-source') but I know some of it was.
So essentially....was there a mass migration of Jews from Egypt? Maybe.
If there was did it happen in the exact way Exodus describes it? Probably not.