Large mammals and birds have disappeared EVERYWHERE shortly after humans showed up. It happened slowly in Africa, where the animals had millions of years to adapt their behavior as protohumans became more efficient hunters, but a bunch of large carnivores disappeared very early as australopithecines/early H. habilis/erectus evolved into the carnivore/scavenger niche. Then Africa essentially stopped developing and most of the remaining big stuff has lasted until now; wildlife numbers today are probably .1% what they were when Europeans showed up 150 years ago.
Extinctions of the megafauna happened far faster, but still over tens of thousands of years, as humans moved into Eurasia and exploded in numbers. It happened in just thousands of years in Australasia and North and South America as highly efficient human hunters moved in, accompanied by dogs, which made them far more effective than humans alone. A bunch of very large birds disappeared from New Zealand as soon as people arrived.
That is not to say that climate didnt play a role in some cases but climates have been shifting back and forth rapidly for the past couple of million years, and all the big stuff lasted through all those changes. Until humans showed up. Same story on every continent, every oceanic island. In spite of various scenarios by which climate changes are held wholly responsible, the near-simultaneous appearance of humans and rapid extinction of all the big stuff cannot be coincidence over and over again. We did it.
Damn, I had to change what I wrote because the preview pane rejected the genus name for Human as [censored]!
