One possibility is that humans out of Africa interbred with the Neanderthals who were already in Europe/Asia, producing the white and oriental races.
With the invention of agriculture, probably in Mesopotamia, white agriculturalists probably expanded out from there, finally arriving at the rich farming environment of the Nile.
There are many scientist who believe exactly what you have written as well. I think it is very conceivable that mating with Neanderthals was fairly common.