Large megafauna around the entire world began dying off both before and after the last glacial maximum, even in areas where there wasn't a significant human presence. The fact that they died off in North America around that time, too, isn't that surprising.
It's also worth noting that at that time, a large part of North America was covered in savanna, which is among the most highly fire-prone habitats, regardless of humans.
Hold on though, because the correlation between “human arrival” and “megafauna extinction” is extremely high. The timeline of megafaunal extinctions goes: Africa, then Eurasia, then Australia, then North America, and finally South America. No points for guessing the order that humans colonized those continents.
In the few historical examples of human introduction to a new ecosystem (New Zealand and Madagascar) within a few hundred years of arrival we’d eaten every animal bigger than a cat.
Groups of humans bigger than 10 can, with planning, catch pretty much any wild animal, even without equipment. Simply digging a hole and tricking the animal into it is one approach.
Obviously the large animals that have a lot of meat (and might knock down your house) are an obvious target to catch.
Island extinctions are a distinct phenomenon. People never managed to drive anything in Eurasia extinct. Even African and Indian elephants still exist. The North American extinction pulse clearly matches the platinum-dust spike from the comet strike.
What about the woolly mammoth, steppe mammoth, straight-tusked elephant, European hippopotamuses, aurochs, steppe bison, cave lion, cave bear, cave hyena, Homotherium, Irish elk, giant polar bears, woolly rhinoceros, Merck's rhinoceros, narrow-nosed rhinoceros, and Elasmotherium to name a few?
How many of those do we have plausible evidence were done in by people?
Of course Irish elk are island fauna. Lions persisted in Europe into the Classical period, finally done in by Roman industrial-scale collection (not comparable to hunter-gatherer hunting).
There have also been large finds with many dead megafauna together. It is not expected that humans at that time had the ability to slaughter very large numbers of megafauna all together.
If humans find a technique to catch a mammoth (eg. lure it into a big hole), then they will eat mammoth meat... But next week, when the uneaten mammoth meat has gone bad, they will catch another.
After a few years, you have a massive mammoth graveyard and mammoths are extinct. Doesn't seem at all surprising.
Large megafauna around the entire world began dying off both before and after the last glacial maximum, even in areas where there wasn't a significant human presence. The fact that they died off in North America around that time, too, isn't that surprising.
It's also worth noting that at that time, a large part of North America was covered in savanna, which is among the most highly fire-prone habitats, regardless of humans.