The evidence is not conclusive for this, but let's run with it. So, prior to what are known as "replacement humans" making a migration out of Africa some 75-50,000 years ago, a first wave of anatomical humans shared the Middle East with Neanderthals, and the Neanderthals enslaved, or at least intimidated, that first wave of humans.
The question you might ask is, who are these replacement humans, and why were the first wave humans not dominant? And the answer is found in the archaeological evidence. The stone tools in use by both Neanderthals and first wave humans were identical and unchanged for hundreds of thousands of years, kind of indicating a similar and static set of cultural tools as well. Given an equal tool kit, the physically more powerful Neanderthals probably had an advantage (see Gods versus Titans myths from all over the world). But then, starting with the late Mousterian tool kit, and progressing into the Aurignacian tool kit, humans using these tools start to occupy sites where Neanderthal tools existed. Neanderthals start to disappear.
Keep in mind, the Aurignacian stone tools are much more various and sophisticated, and are associated with the so-called Cultural Big Bang, when the first cave art, animal figurines, and probably rope, twine, and textile objects appear (base on the prevalence of fine bladed flint, bone needle, and fish hook tools).This Aurignacian Efflorescence really took off in a big way, and practically every habitable surface of the Earth was populated in a few short millennia. Many suggest this cultural sophistication was the result of language.Oh, bullshit. There is plenty of anatomical evidence to suggest language predated the Aurignacian Efflorescence by several hundred thousand years.
So, what did it? Genetics? Hardly.
My answer? Bows and arrows. And a peculiar form of psychopathy that exists to this day, perhaps best made manifest through our habit of genocide. We ape versions of solenopsis invicta, armed with our projectile stings, swarmed out of Africa to conquer the world.