I'm sure killing a mammoth with a spear works, and trying to kill it with a bow and arrow wouldn't.
Grog say campfire make flat world warming. Only 5.35 years left.
Who knows if the Neanderthal had those but it is possible.
The weapon is unknown in Africa (as far as we have found) but suddenly pops up all over the rest of the world

I’m sure killing a mammoth with a spear works, and trying to kill it with a bow and arrow wouldn’t.
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True. But if a group of humans encountered a group of neanderthals—the group with the bow and arrows would be dominant. Because at first the neanderthals would not even know what hit them.
That would cause the kind of fear that would cause the Neanderthals to shink from contact with humans.
That would also explain why for the first time neanderthal ranges shrank into ever smaller pockets.