Hmm, for me it's not that they'll turn out "okay" necessarily, but more so that things will just... continue. Like, if we fuck up the planet to the point we won't be able to survive on it, eventually the ecosystem will recover, just without us. Things will continue, we might just not be there to see it.
This meme gives an example https://m.funsubstance.com/fun/644237/some-people-have-a-problem-for-every-solution/