“... assuming Adam and Eve were Caucasian ...”
Well, no, I don’t think anyone assumes Adam and Eve were Caucasian. Why would anyone think so? Why wouldn’t they look Middle Eastern or North African?
If we assume that God created a perfect world, and Adam and Eve were perfect when created, then there would be no defects for them to pass on at first. If we assume corruption entered the world at the Fall then disease and defects would start to appear. So there might not have been enough generations for many defects to develop by the time Noah’s family came along.
Since every human extant came from Adam and Eve,
they had to have all the necessary genetic information to produce every human trait we see.
“Caucasian” is simply one of the resulting trait combinations after the split at Babel.