> There was this idea that humans arrived and killed everything off very quickly—what's called 'Pleistocene overkill,'" said Daniel Odess, an archaeologist at White Sands National Park in New Mexico. But new discoveries suggest that "humans were existing alongside these animals for at least 10,000 years, without making them go extinct.

I don't think there is a contradiction here. Indeed we could have them get extinct, it just took a long time by human standards, ~10 millennia. I don't know how many mastodons or giant sloths/armadillos there was in Americas before humans made landfall here. But I'd guess about 10 million of each. If they took about ten years to reach sexual maturity, that gives us about 1000 generations of megafauna in this time window. To get their population down from 10 million to just one in this time, each generation had to be smaller than the predecessor, but on average could still retain log(10^-7)^-1000 ~= 98.4% of its size. Even if stone age tech enabled humans to overhunt them consistently only by a slight amount, ~1.6% each generation, they still would end extinct in 10,000 years. So it was not "without making them go extinct". It was "while making them go extinct.".