we have skelletons or bones
modern human was 200.000 years old in Africa
first modern humans were in SW Asia about 125.000 years ago : that was Eemian interglacial : not after last LGM but right after GM before LGM
modern human meat Neanderthal 80.000 years ago, modern human could not compete with Neanderthal in Europe and Central Asia
then modern human developped new tools : blade stone tools 50.000 years ago and then modern human expanded very quickly
so 40.000 years ago Neanderthal got extinct
during LGM many humans died, and after LGM new expansion started