In act, the Torah, and Bible IS proof - it is even accepted in courts of law.
However, this is one major thing that is not (yet) supported by other evidence. There are some good reasons - how many writings are there in your local newspaper, or historical reviews on the people that take your garbage to the dump? Or, that work on the city sewage system? Probably few, or, mostly likely, none. Well, the Jews were slaves, so, even lower than the people I mentioned.
We know about ancient Egypt mostly in the monuments that were left behind. The tombs might show life scenes, but, the writing is all about the kings, or important people depicted. There is virtually nothing regarding the slaves. E.g., it was assumed that the pyramids were built by slaves until only about 10 years ago, when the worker's villages were discovered. So, even the people who built the Pyramids were unknown until very recently, and precious little is known about them, despite being craftsmen, and so on, working on such huge, and important projects. So, how could we be expected to know about slaves?
There's more. Paper only lasts a few hundred years, at most. And, even then, it has to be stored properly. Paper from 3 or 4000 years ago is long gone. The evidence we have comes from carved stone, or, perhaps clay tablets - those that haven't broken, or crumbled by now. The Egyptians simply made no monuments to slaves, nor recorded anything about them in stone. Which only makes sense.
The chances of finding anything about any slaves in ancient Egypt is pretty slim, and that includes the Hebrews. The only people this was important to was the Hebrews themselves, who carried the story with them, and eventually wrote it down.