What evidence is there that the Earth is a perfectly sustainable ecosystem?

There have been ice ages in the past and asteroids might crash into the planet in the future. The ice caps are melting and ocean levels will rise. The ozone layer is being depleted. Species go extinct. Most of it is blamed on humans.

Maybe the Earth wasn't meant to last as long as everyone hopes it will. What evidence do we have that it would last a lot longer if humans weren't around?