Milankovitch cycles.
This chart shows how the temperature on Earth changed over millennia before Common Era. The unit of time scale is Ka that is thousand of years. This is the sum of several cyclic processes. 2 major components have periods of approximately 100 Ka (maximum marked 1, 2, 3) and 41 Ka (4, 5, 6, 7). The last maximum of temperature was 8000 years ago.
Vostok insolation.
This is the same with a more fine time scale, only the past goes rightwards from present.
Neanderthals ceased to exist approximately 30000 years ago. This corresponds to the extremum on Milankovitch cycle with the period of 41000 years. If the maximum of temperature was circa 10000 years ago, that was the previous minimum. You see 3 cycles of deterioration: 2-5, 5-4, 4-1. That was the worst time from the last 125000 years. Neanderthals disappeared when living conditions worsened so seemingly it was natural, gradual extinction.
39000 years ago the supervolcano in Italy near Naples terminated life in West Europe. Meanwhile, advancing population of modern humans from Africa pushed Neanderthals in the quite definite direction. Namely – to the East. From East Europe they came to South Siberia and finally could reach the Pacific coast. We get confirmation for this immediately. The Ainu people of Pacific islands and the continental Far East were strikingly different from their Mongoloid neighbours, but look very like North Europeans.
Ainu man, circa 1880.
They stored their own legendary history and insisted that they live in these places tens of thousands of years. Also their lifestyle was recorded in the early Japanese chronicles. This description perfectly fits what should be expected from Neanderthals. They were physically stronger, had violent behavior and quite specific image of life. It was clearly advanced, but not a civilization in common meaning. They did not practice production in our sense. Instead, they tried to use natural resources rationally and regulate own consumption and population.
This migration could also reach America. Archeology of Native Americans show wonderful things. There existed a widespread cultures which created large earth structures.
1840s map of Mound City. Hopewell culture.
Similar structures were found in Britain, South Ural and they may be predecessors of Scythian curgans and early Egyptian pyramids built from earth and mud bricks. Also America knows numerous reports of giant human skeletons circa 2.5 m tall.