Well, yes you could find several cites…the “Overkill” hypothesis certainly has a lot of support. But you’ll also find lots of people who think it it climate. But of course, since we have a climate change at the same time as humans move it, this is something where you can’t really tease out the contributing factors without a time machine.
It is suggestive that the large animals started dying out in Australia before the end of the Pleistocene, just when humans were moving in. The giant diprotodons, marsupial lions, mainland thylacines and devils, giant kangaroos, etc, etc, all went goodbye. And when humans moved to New Zealand, goodbye to a dozen species of moas. Oh, the kiwi is a dwarf moa! So we still have one moa left! And when humans moved to Madagascar we suddenly lose the elephant bird (pretty much like a moa, but heavier), the giant fossa, and dozens of lemurs…including one that had a cranial capacity near a chimpanzee’s!
So the theory that without humans the megafauna would have survived is accepted by a lot of people. But maybe we would have lost most of these things anyway…most also died out in Europe, where they have been living with people for tens of thousands of years.
Recent archaeological digs indicate that man first arrived in the Americas 30,000 years ago, well before the last ice age. (Some finds in S. America and one find in NE USA.) But even if so, they apparently were not that numerous, as few evidence hasa been found.
Usually a species becomes extinct due to some catastrophic event, such as the asteroid polluting the atmosphere and wiping out the dinosaurs. I believe similar events occurred previously, eliminating other species.
In any event, that is a question which is unsolvable, so we can conjecture all we want.
First off, it is not true that most species go extinct due to catastrophic events. It is true that there are certain times when large numbers of species go extinct all at once, and those are almost certainly due to catastrophes. But most species go extinct during normal geologic times.
And yes, there have been several mass extinctions, the one that killed the dinosaurs was only a moderate one. The most severe one took place at the end of the Permian (right before the age of dinosaurs). It killed off the trilobites, and all the mammal-like reptiles. Mammals have been around much longer than dinosaurs…in an ironic twist, the early primitive mammals were wiped out, making room for the dinosaurs, who were wiped out, making room for the mammals. But 90% of all species went extinct at the Permian event, only 50% or so at the KT boundary.
Next, the 30,000-35,000 year old sites from south america are not well authenticated. I would say that most archeologists think that they are not really that old, of course there is disagreement, that’s what science is about, but I’m pretty sure that they will eventually be disproved. The thing is, it just doesn’t make sense. We have archeological evidence from 35K years ago, but not from, say, 25K? Unless the american humans from that time went extinct (which could have happened) it doesn’t make sense.