

There was organized violence deployed by groups of humans against other groups of humans long, long before anything we would recognize as warfare. Particularly brutal violence too, because the objective was not to conquer other people (something which only makes sense once agriculture is the dominant mode of sustinence), but to either drive off or exterminate a rival group so you can use their territory for yourself.
And we don’t even need to talk about people here: we have records of chimpanzees fighting small scale wars of harassment and extermination against neighboring groups.
Pre-modern, pre-civilization, pre-aggriculture, pre-you-name-it human life was far more violent than what we deal with today.
Nomadic people don’t just wander around aimlessly, and there are big differences in how desirable different territory is for nomadic hunter-gatherer humans. The principle is the same as with nomadic pastoralists: your group has a territory which can sustain them when hunted on/gathered from/grazed/etc over the course of the year, and your group will wander within that space in a deliberate pattern. If some other group decides to “just move on to” your group’s territory, hunting the animals and foraging the plants that your group knows they are going to need to survive the year, that’s an existential threat to you. And you can’t “just move on” yourself without wandering into the territory of yet more groups whose territory borders yours, and who will react violently to your presence for the same reasons.
Given the choice between fleeing to who knows where and fighting who knows who for the privilege of moving, or staying right where you are and fighting for the land you know your group can survive on, you stay and fight.
Humans spread out across the earth as the losers of these conflicts (those who survived, anyway) fled until they stumbled on new-to-humans territory, often displacing or eradicating groups of more “primitive” hominids they found there. This process continues until just about everywhere which humans can reach and which can support human life has humans in it. But expanding populations, the occasional natural disaster, and normal human frustration that their territory sucks while their neighbors have it great (which was often true; again, not all land is the same to a nomadic hunter/gatherer) meant that these conflicts were constantly reignited.