Climate science isn't falsifiable though. We cannot go back to the year 1600 and rerun the last 400 years without human industrial activity but keeping everything else the same and observe how the climate differs.
Just because one can imagine an impossible experiment does not prove that a “science” is not falsifiable. There are lots of predictions that climate science makes that are falsifiable. And one can imagine that at some point in the future, we will be able to do experiments on appropriately paired sets of planets.
The phase “unfalsifiable” is often used to suggest that something is not scientific. My recollection is that Popper thought that evolution was not a scientific theory for the same reason. But unfalsifiable depends a lot on the kinds of experiments that are possible, or might become possible in the future.
Not sure why you are getting downvoted. It is a fundamental challenge of climate science. You can backtest a model all you want, but anyone familiar with confronting backtested models to reality knows that this gives you very little comfort. Climate science fundamentally deals with untested mathematical models.
It is not the only domain of science that has this problem. Medecine is a big one. You can experiment to some extent but for obvious ethical reasons, there are lots of stuff you can't experiment on, and as a result we keep getting contradictory studies on issues that should be purely factual.
The phase “unfalsifiable” is often used to suggest that something is not scientific. My recollection is that Popper thought that evolution was not a scientific theory for the same reason. But unfalsifiable depends a lot on the kinds of experiments that are possible, or might become possible in the future.