There is a huge gap between the time modern humans left Africa and the rise of the ancient civilizations. Genetic evidence for the migration out of Africa dates it to around 60,000 years, while the oldest civilizations are less than a tenth as old. So there is really no connection between the two – these events are very far apart in time. A lot can happen in 50,000+ years.

The most obvious difference is demographics. Before 60,000 years humanity was almost entirely confined to Africa. But by 6,000 years ago, far more humans lived outside Africa than inside. If civilization is likelier to arise where there are people, then statistically it was likelier to arise in Asia.

More generally, “civilization” isn’t some magic mark in time, it’s part of a continuum of changes through the Holocene. The antecedents of civilization are sedentism, which goes back to the Natufian culture spread across the middle east, going as far south as the Sinai, which is pretty much the border of Africa. The technologies needed for civilization were agriculture and the domestication of animals, which happened in southern Turkey. The foundations of civilization were the societies which first adopted these technologies and made them practical. These were the PPNA (Pre-Pottery Neolithic A) and PPNB, a diffuse collection of sites spread over the middle east, and yes, they extend into Egypt.

Even “civilization” itself is not so precisely dated. There is very little difference in time between the Mesopotamian and Egyptian civilizations. Yes, the oldest sites we know of are Mesopotamian, but the difference is minor. Is it even real? Perhaps the oldest Egyptian sites remain to be discovered, perhaps they are buried under sand dunes as Egypt slowly desertified. Maybe they were contemporaneous, maybe Egypt is even slightly older.

At any rate, I wouldn’t make a big deal out of which was the “first civilization” – Mesopotamia or Egypt. The big contributions to civilization came from both Egypt and Mesopotamia. We used to think the Mesopotamian script is older, but new research shows that Egyptian might be just as old, or even older.

Or you could look at it as a cline produced by the diffusion of technology. If agriculture or animal domestication originated in the hills of southern Turkey and if these technologies diffused outwards from there, then Mesopotamia is closer to the origin than Egypt. Do we need any explanation beyond simple geography to explain why it arrived in the closer place a couple hundred years before the farther place? Does it really say anything about “Africa” or “Asia”? These terms were meaningless back then.