The evidence is there, particularly when Egyptologists are agreed that the Israelite sojourn in Egypt and exodus from it would be the middle Bronze Age. An archaeologist called David Rohl has written extensively on the evidence in Egyptian artifacts that prove the Habiru (Hebrews) were indeed forced into hard labour in Egypt after a series of weak 13th dynasty pharaohs followed Amenemhat III (who was the pharaoh living at the time of Joseph.)
Rohl has discovered Joseph's palace at Avaris in the part of the Nile delta known in the OT as Goshen. The Hebrews were at first welcome in Egypt and became very influential. Wealthy Semitic graves at the middle Bronze Age level have been found at Avaris. Joseph was entombed in a small pyramid in the grounds of his palace, with a chapel containing his colossal cult statue. This depicts an Asiatically pale fellow with reddish hair adorned with the multicoloured coat of a middle Bronze Age chieftain.
Then the Hebrews became despised and pressed into hard labour. Bronze Age documents have yielded up pharaonic slave lists with Hebrew names, and the tinpot grave goods of an underclass were found at Avaris. Independent dating of Rohl's bold chronology vindicate his dating of Joseph's pharaoh, Amenemhat III at 1678 BC give or take 4 years. The result was 37 out of 39 lunar month-length matches, whereas orthodox chronology scored no better than 21 matches.
The astronomer Dr David Lappin, of Glasgow university, concluded, "Most of the astronomical data... simply do not fit with the orthodox chornology, while the support it gives to David Rohl's new chronology is nothing less than startling." Rohl also found water heights chipped into cliff faces just south of the Nile's second cataract that account for four massive Nile floods that would have made seed-sowing impossible for several years, and famine inevitable. Joseph's God told him of this coming famine, giving him the interpretation to pharaoh's dream, and Joseph was put in charge of preparing for, and surviving the famine, which also lead to Joseph's family moving down to Egypt - the start of the Habiru population in Egypt.
So although the Egyptian records don't relate the historic event of the 10 plagues and the exodus of the despised Habiru, Egyptian records do, indeed, point to the truth of the biblical account. The proud Egyptians would never conceed, in writing, that their gods were humiliated by each of the 10 plagues, and their forced labour work-force left with great wealth! Rohl places the Moses account during Ramesses II rule, with Moses then having to deal with a new pharaoh, Merenptah, at the time of the Exodus. There IS evidence, for those with eyes open to see it and the will to re-arrange chronology according to known facts!
EDIT - No, I didn't say the Egyptians never recorded anything catastrophic to their nation. No record of the Habiru exodus has yet been found; it might never have been recorded, especially as that pharaoh's army was drowned at God's hand, but it also might have been recorded and is awaiting discovery. Please don't try to put words into my mouth.