The Mediterranean isn't exactly the Atlantic or Pacific Oceans. A small boat could go to Southern Europe without much trouble. God, Tom Sawyer could have likely gone to Europe on his Mississippi raft!
With that in mind, I think it was one continuous stream of Africans going on a Sunday School picnic to Southern Europe.
If no one noticed, Southern Europeans often have brown eyes and curly brown hair. This is not a nordic trait.
I think many Europeans are just African Light.
Hmmm...The Adventures Of Huck and Jim On Mare Nostrum....yeah I'd read that.
A very nice article from National Geographic about the Nubian Kings and the relationship with Egypt:
See also the little caption on the right-hand side about Black Pharaohs. Very interesting.