You have read the book of Numbers, I hope? It tells us how many there were in each clan, and the figures add up to 600,000. We can be sure this figure is accurate because it I s firmly reiterated several times.
Jim, I wanted to emphasize that I don't hold to the theory that Rameses II was the 'Exodus pharaoh'. Neither that the Israelites built Piramesse for him. I think Exodus 1:11 may be referring to Avaris, but need to look into it more.
So why on earth would Exodus refer to Hutwaret (Avaris/tell el dab'a( as "Ramses"?
If you're going with an earlier date for Exodus (for which you've provided no evidence), then you can only mean dyn XVIII and the reign of Amenhotep II.
We've already been there: Egypt had pushed out into Canaan already - and further. An escaping tribe would have been wasting its' time settling there if it wanted to get out of Egypt,.
Even if you add on the proverbial forty years, that makes things even worse - because Egypt's borders had stretched to what is now Turkey.
And if you want to go into semantics, why would an Egyptian king of the mid eighteenth dynasty, who was either tied to, or promoting, the cult of Amun of Thebes name a city for Ra of Heliopolis?
We already know Amenhotep II built minor shrines to Amun at Hutwaret, and further north at Bubastis, Xois, etc. He even left dedications to Amun in the Sinai and what is now southern Israel.
There's evidence of him enhancing the Re temple at Heliopolis and Memphis, but that's about it.