That said, the same is true of nonviolence.
We walked out of the Cold War alive. Humanity has faced extinction before, and despite it all, we walked away alive last time. It's not unreasonable to think we can do it again.
I'll answer with a quote from the founder of the Rationalist movement, Eliezer:
"How certain do you have to be that your child has terminal cancer, before you start killing puppies? 10% sure? 50% sure? 99.9%? The answer is that it doesn't matter how certain you are, killing puppies doesn't cure cancer."