Thats not how it works. Human population because it has no predators grows rapidly until it reaches it’s carrying capacity. Carrying capacity is high in a place with lots of food, living space, etc and low in a place like a desert.
You are thinking of exponential growth when population is actually logistical growth.
I'm curious to know if anyone has OBJECTIVELY modeled human population growth from the pre-historic period to present. If OBJECTIVE analysis could possibly be used in this highly political field, it may shed some scientific light on the theory.
Also, why would humans emerge from a desert unless stress makes them think better to survive.