Almost impossible to say, we have a good capacity for surviving, it is hard to imagine a disaster so bad that some few humans would not crawl out of a cave somewhere in a mountain valley, and start over, without that disaster being so bad that it destroyed almost all multicellular life. On the other hand, that which we call advanced civilization could be very fragile.

So that perhaps a better, pair, of questions would be. Can civilization survive into the future? And. Can the biosphere as a whole, excepting perhaps bacterial life, survive into the future?

( One irony is of course, that one of the things which could really save us and civilization, may well be a major disaster, say a disease like the current virus, but much more damaging, which would relieve the world of say 99% of our population. Given that we have used up so many of the worlds resources, recovery would be slow, perhaps slow and measured enough to save us from making the same mistakes again. But that I think is a dream, not likely to happen. )