The Santa Elena Rock shelter people have been making this argument for years now. Between the questionable lithics, dating, and excavation methodologies they don't have sufficient evidence to support the claims they're making and they've offered no convincing explanations for why the standard of evidence should be lowered given the massive chronological issues their dates would suggest (<5000 years after Yana 10k miles away!).

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.".

By comparison, we killed off the Dodo in, what, less than 10 years?

I think it’s fair to talk about 10,000 years as a long time. Sure it’s barely a blink in geologic time, but we’re talking about the human perspective here.

It took humans quite a bit longer to drive say, the tarpan, to extinction.

You can look at modern game animal populations to see how the feedback loops work.

Those tools were really valuable. They busted their butts, making them, and wouldn't want to toss them aside, just because they got chipped or cracked. They are much more likely to throw them into a "spare parts bag," and keep them around.

Today's throwaway culture is actually pretty new, in human history. Just hang around some poor folks, to see radical conservation, in action.

The other possibility, is that most of their tools were composed of biodegradable stuff, like wood, bones, and shells.

In Africa, they used wood and raw iron for their stuff (I have spears, shields, and arrows, from there). That doesn't tend to age well.

If you walk the mountains of Nevada along the fossil shoreline where the Lahontan[0] civilization thrived, you will regularly find large quantities of neolithic trash strewn about. Broken, half-finished, or abandoned stone tools are ubiquitous. It takes little effort to find obsidian arrowheads, some in perfect condition.

The preponderance of the evidence is that these were viewed as disposable artifacts, use once and throw away. If they were actually valuable, they could have picked these up in the same way we pick them up today. It would have essentially been "free money" lying on the ground. Yet for some reason, in all the intervening millennia, so few people did that modern humans can find them everywhere.

[0] https://en.wikipedia.org/wiki/Lake_Lahontan

No, modern sloths are not descended from giant ground sloths. The rest of the article might be okay, but it's hard to trust it after a mistake like that.