You know your Egyptian timelines.. Very good.
The problem with the Old Testament - particularly the Torah those books that were attributed to Moses - is that that were written from 7th century to the late 6th century or to mid-5th century BCE.
There were no 2nd millennium BCE written scriptures called the “Genesis” and “Exodus” in this time period, the Middle Bronze Age and Late Bronze Age.
For instance, paleo-Hebrew (ancient Hebrew) alphabet didn’t exist until the around the 10th century BCE (eg the Gezer Calendar and the Zayit Stone). These are the earliest literary evidences of Hebrew writings, but it make no mention of anything in regarding to Genesis and Exodus story, no mention of any kings (eg no David and Solomon, no Rehoboam and Jeroboam), that ruled at the time of these inscriptions were written.
Before this was Proto-Canaanite alphabet (12th and 11th century BCE), which paleo-Hebrew alphabet were derived from.
But in much of the 2nd millennium BCE, the most common way of writing (from Canaan and Syria to Babylonia and Elam) were the cuneiform, not the alphabet.
The invention of cuneiform probably originated in the city of Uruk, in which most translations of Genesis 10 referred to as Erech, a city supposed founded by Nimrod, a great grandson of Noah.
The writing is pre-Sumerian cuneiform, or what experts called proto-Sumerian, have been dated to 3500-3400 BCE, where it was found at Uruk IV.
Sumerian proper, started with Jemdet Nasir period (3100 - 2900 BCE). Much of The 4th millennium BCE called this period the “Uruk period”, c 4000 to c 3100 BCE, which coincide with use of both stone and copper tools, Chalcolithic period.
Like Jericho, Uruk was repeatedly built over older layer of the city. And the earliest layer, Uruk XII was built around 5000 BCE, so really the whole Nimrod and the Tower of Babel episodes are clearly false.
But going back to Egypt. There are no evidences to support that Israelites were living as independent and then as slaves in the 2nd millennium BCE, no evidences to support the Hyksos were Israelites or Jews. And there are no evidences to support Joshua conquering Canaan, after Moses’ death.
The Exodus’ Rameses just highlighted another thing wrong with book, contradicting archaeological evidences.
Another error is that of Genesis 10, which also claimed that Egypt didn’t exist until Ham’s son Mizraim or Egypt was born. Egyptian culture predated the 1st dynasty of Egypt. And if the Flood falls some times in the 2nd half of 3rd millennium BCE, then the pyramids of Saqqara and Giza would also predated the Flood, which would make Genesis claim false about Egypt.