I think we're past focusing on proof. We need to focus on probabilities and insuring ourselves against possible or likely outcomes.
Reality check, we have a sample size of 1. So, if we get it wrong, it's game over and we mess up our planet for centuries or millennia. The question is how comfortable we are with being utterly wrong on that gamble. For me the answer is, pretty damn uncomfortable.
Even a 1 % gamble on getting this stuff wrong has a pretty significant chance of backfiring on us. Russian roulette has only a slightly worse probability. And to be fair, our odds might actually be considerably better putting the proverbial gun to your head considering what some scientists are saying. Are they 20% right 50% right or 80% right? I don't know. Is the water going to rise 1 m by 2060, by 2100, or later? I don't know. I do know that would be highly annoying for a lot of people and it would be awfully nice to live in a place that has dikes or is well above sea level by then.
I happen to believe it is probably ballpark closer to 95-99% but I'd argue even a 1% chance that they are not completely wrong about this should be more than enough motivation to do something about it on the off chance it is needed.
The number doesn't actually matter that much. What matters is acknowledging it is not 0%. We have a non zero, potentially very large chance that we are actively killing this planet and everything on it in either the next decades or centuries. That's too big of chance to just go "Meh, lets wait and see". As soon as you acknowledge that, opposing any action that mitigates that risk becomes madness.