Citation needed for evidence of human cooperation at this scale. As you say, climate change is slow moving, and there's no real evidence across the last 60 years of knowing about it suggesting humans are willing to do what it takes to survive it.
"Humans move" is one of the easiest things to predict. The biggest problem today is that they generally move to somewhere that other humans are already in, which is of course rather lessened by any major disaster wiping out a majority of the population.
...people to move to the poles/into caves/beneath the ocean/whatever