We don't know that. It seems to be a leap of faith, based on the possibility of numerous successive achievements (IA, then fusion, then robots, then interplanetary mining, etc.) where each new step is always reachable. Like in a video game.
Maybe the necessary amount of oil (or whatever) required to reach the next key milestone towards unlimited resources has never existed. Maybe it'd have required 1 billion more years before humankind reached the industrial age.
Maybe the trees on our island are just enough to build a raft, not a brig, and we should have used them to build a shelter and make the inevitable end more comfortable.