They do have ways of “experimenting” in such situations. For one thing, our current climate change is a “natural experiment.” That is we are applying the treatment (emitting GHGs), and we can study the before and after.
They have very sophisticated techniques for studying climate and it is quite scientific, looking at all the known and quantifiable factors, and tweaking their models and understanding as better evidence & theories come forth. They use a “bayesian” approach, which I believe is to study the situation as it exists and factor in all the factors. Then they can artificially “remove” a factor, such as the increased CO2 to see if they would have gotten the same results. What they have found is that it is very unlikely they would have gotten that same results (our current state of the climate) without the enhanced GHGs.
Same way re extreme weather events. They are now (for the past few years) able to say that the increased extreme heatwaves, floods, and droughts around the world is way out some 3 or more standard deviations (less than 1% probability part of the tail) away from what would be normal without global warming.
Now my problem with science is that in striving to avoid the FALSE POSITIVE (making an untrue claim) it is too conservative and reticent, requiring high levels of confidence (usually 95% confidence) before making a claim.
In the case of serious threats to life on earth (or cancer) I prefer to avoid the FALSE NEGATIVE (failing to address a true harm); I don’t need 95% confidence, I don’t even need 50% confidence. As a prudent person, I even have home and car insurance, even tho I don’t really expect to use these, but you never know…
So call me a prude, extremely conservative. That’s just me. I don’t gamble with people’s lives. I don’t even like gambling with money. Tho I’ve done it a bit, but once we lost the $50 in Vegas, we called it quits.

The idea of gambling with other people’s lives and property is extremely distasteful to me – like playing Russian roulette, only 19 of the 20 chambers are loaded with bullets.