The issue with that is the weather conditions in North Africa weren't always the same as they are today. In fact the Sahara just 9,000 years ago wasn't a desert but instead a lush green savanna no different than what you see today in most of tropical Africa.
Paleoclimate and archaeological evidence tells us that, 11,000-5,000 years ago, the Earth's slow orbital 'wobble' transformed today's Sahara desert to a land covered with vegetation and lakes.
www.nature.com
You had tropical animals like hippos, elephants, and giraffes roaming North Africa. You also had humans living among them that depicted these animals in rock art.
A civilization like Ancient Egypt rising up after the Sahara dried up actually makes sense when you think about it. People had to run to the only water source that remained which turned out to be the Nile. And it was around the Nile the civilization flourished. Also the mixing of races also makes sense if you think about the fact as the regions across Southwest Asia also began to turn into the desert, some of those people went down to the Nile where they encountered Africans and began to mix with them.
