Humans entered a Europe after Neanderthals were already well established. Why did Neanderthals vanish. Given human nature, it’s hard for me to believe there wasn’t a fair amount of conflict between the two groups, but you needn’t assume humans wiped Neanderthals out. National Geographic offers an alternative explanation consistent with known facts,
Unlike Neanderthals, humans had spears and bows and arrows, weapons that could kill from a distance. And also unlike Neanderthals, humans had dogs, or at least something between wolves and what we think of today as dogs. These wolf-dogs, as the article refers to them, helped humans hunt successfully. As the Ice Age intensified, an edge in hunting gave humans an edge in survival.
Add into that mix the doggy traits of being able to run for hours much faster than we can, track an animal by its scent, then with a group of other wolf dogs surround the animal and hold it in place while you tire it out. The advantage for wolf dogs is that humans can come in and kill from a distance. The wolf dogs don’t have to go and kill this thing with their teeth, thereby lowering the risk of injury and death from very large animals like mammoths. For humans, it meant you could find the animals a lot quicker and kill them more efficiently. More food, less risk, faster.