A significant number of mega fauna species is hunted to extinction whenever humans arrive.
> If your evidence is the total extinction of American megafauna
The evidence is the extinction of most American megafauna species.
> In fact, you potentially argue for the opposite: in clearing some megafauna but sparing others, humans did indeed carve out a potentially sustainable ecological niche, which their continued presence helps to prove was sustainable.
Humans have continued to survive everywhere, so that is evidence the the presence of humans everywhere has been sustainable.
The comment making the claim about indigenous societies in the Americas is that they are "ecologically compatible". They are compatible with an ecology they altered. This is, again, true everywhere. You might argue that industrialisation has changed this as a (relatively) stable state is not reached because of continuing rapid change, but it was true before industrialisation.
> I'll suggest a third option: humans hunt megafauna to extinction in the presence of conditions that favor such behavior - perhaps climatic, geographic, and/or cultural. So, it happens. But it doesn't always happen.
I have two objections to that:
1. Its not all megafauna, it is most. Some species can survive humans.
2. The extinctions have happened across many different climates and cultures and on every continent and many islands.
It is not proved beyond doubt that humans have always caused extinctions, but the pattern is very consistent, which makes it by far the most likely explanation. Even where hunting is not the direct cause, many things humans do (such as agriculture) will destroy their habitats.
Where humans did not arrive until much later than most places (e.g. in places such as New Zealand or Madagascar) megafauna survived until after they did, and were then gone with a few hundred or a few thousand years.