The absence of any such evidence, while not conclusive proof of course, constitutes evidence against this event happening.

There is documentation in Egypt of slaves around this time, and of the subsequent departure of some unstated number of slaves. There is evidence of pig bones disappearing from trash sites on the path of the migration, and there is evidence of a shift in religious practices along the migration path. So there is some evidence of an event similar to the Exodus occurring.

We're talking about something that occurred over 3000 years ago. Most events back then weren't recorded, and even then it was still so difficult and time consuming that Egypt and Ancient Greece generally left out the embarrassing parts, most of which we only know about because their contemporaries wrote about it to disgrace them (and most historians now suspect that the vast majority of negative accounts of other civilizations were wholly made up, especially those written by the Ancient Greeks).

Very few nomadic migrations left evidence on the way. There is more evidence of the some sort of exodus having occurred than of the human migration from Asia into South America (note: an increasing number of historians claim the first migration was by sea from Africa, not over land from Asia).