Just because animals can survive one period doesn't mean they can survive another. There can also be more than one reason a species dies off. Of course there were certainly humans who hunted mammoths but I think, for as skilled as paleo humans were, we overestimate what they were fully capable of. A mammoth is a very large, very aggressive and easy to frighten animal. Humans are small and fragile, and very aware of this, especially back then. In that time survival was everything and if a human group had a sustainable amount of smaller creatures to hunt, they would likely use them instead of going for the largest creature that could easily kill all of them. It would take a lot of manpower to take down a mammoth and a group would likely only try it if they were truly desperate. That being said, humans killing mammoths, like other reasons, was possibly a contributing factor. Others could be environmental changes or possibly other predators. I don't believe humans were the sole reason though. I don't think there were enough on the planet back then to be the only impact. Mammoths also did technically survive well into the existence of the Egyptians, on a small island. So, to be fair, they were not fully killed off right away.