Even after primitive Homo sapiens broke out of Africa 200,000 years ago, it took over 150,000 years to conquer Neanderthal lands. In Israel and Greece, archaic Homo sapiens took ground only to fall back against Neanderthal counteroffensives, before a final offensive by modern Homo sapiens, starting 125,000 years ago, eliminated them.
This wasn’t a blitzkrieg, as one would expect if Neanderthals were either pacifists or inferior warriors, but a long war of attrition. Ultimately, we won. But this wasn’t because they were less inclined to fight. In the end, we likely just became better at war than they were.