The Highbrow Neanderthal

But what if there was more evidence? Well there could be if we were willing to instantiate a Neanderthal genome in vivo…

So our ability to walk long distances in moderate to high temperatures is what allowed us to thrive on the plains vs jungles of Africa, before we were modern humans.

As far as modern humans go, it wasn't a single wave of migration, or even multiple waves of migration. The more we learn the more we realize it was more like diffusion of increasingly advanced culture across a mesh that pre-existed across the globe.

Our distance endurance was literally useful for traveling to new and better places as hunter gatherers, or simply following seasons. But it also enabled very specific tactics like persistence hunting or steering entire herds into human designed funnel traps. Near as I can tell from reading these were pretty key to our rise at a critical time.

Then of course, language and the accumulation of knowledge it enables was the huge jump to modernity. We'd like to think we're far past that jump but we really aren't, we've just gotten so good at cracking rocks against each other now they're on the cusp of thinking the same way we do.

At looking for clues about why those initial waves went exting, maybe we could take a look at how more recent tribes or even old civilizations like Incas, Mayas, etc. made it through a couple of centuries, and eventually got "extint".

Some of those groups were surrounded by other tribes, and tried to expand their territories, with different outcomes.

Some didn't tried to expand, they just got well adjusted to their original territory and didn't need more resources.

But everyone in those groups eventually disappeared from history.

Even when the american continent was discovered, the remaining "true" mayas didn't remembered or indicated that those big monuments, cities ever existed already taken / hidden by the jungle. Many of those also, were just found literally hundreds of years after having seen the last true mayas.

Then the original Neanderthal civilization had a sharp edge over the Sapiens, through thousand of years.

Ok, everyone says here "but technological development SHOULD have happened". And I would say "not necessarily", and it actually could happened a couple of times, but it didn't had the written word advantage to keep building upon learned stuff (you keep discovering-then-forgetting the same things over and over), or maybe there was other factor limiting the Neanderthal technological development (neurological, strong "bad-to-tech" cultural practices, etc.).

You say "not probably", but Homo Sapiens just recently (re)learned to wash hands as a safe method to better health outcomes, maybe for the 40th time in several thousands of years across a dozen of civilizations / tribes who already know about washed-hands = good health:

https://es.wikipedia.org/wiki/Esenios