Try this post (off-site). It posits a chronological model using the MT, but modified with the LXX, SP & Josephus where they differ for seven post flood patriarchs. The difference puts the flood back 650 years to 2953 BCE. (WT places the flood at 2370/69 BCE. But that is based on a 1513 BCE exodus and a 997 BCE split in the kingdom of Israel. Nor does it take into account any differences with LXX/SP/Josephus.)
The chart in the link is premised on an exodus date of 1446 BCE, and 430 years between the covenant with Abraham and the exodus. This places Jacob and his family in Egypt for 215 years (based on Ex 12:40-41 LXX/SP)
The post just before the linked one has a link to a population calculator that will allow playing with the numbers. A couple of factors that may skew the population calculator are the wider spread practice of polygamy and the longer lifespans reported in the Bible for the several centuries after the flood. These factors would tend to cause larger populations.
It is interesting how population growth is exponential in nature. Small increases in birth rates, over lengthy periods, can produce huge differences in population.
Just for some example numbers: You could start with 8 (post flood survivors), and about 400 years to the building of the tower at Babel. Or about 1500 years from the flood to the exodus. (The Torah reports roughly 600,000 grown men in the Israelite camp at the exodus.)