What a provocative question - I have a feeling this could be an equally useful historical test case as the invention of the airplane and hot air balloon. There might be an even larger number of historical contingencies here than it seems at first glance.
It seems important to split the question into two parts:
It took 10 years from mass residential refrigeration to lead to use of CFCs. It took another half-century to detect atmospheric CFCs and the damage they were causing. Bans started taking effect almost immediately due to environmentalist groundwork on pesticides that had been taking place over the previous 15 years.
If I had to try and make some sense out of this, it took a lot of economic growth and refinement in refrigeration technology and chemistry to motivate mass use of CFCs. That same growth and use of chemistry was wrecking people's health and the environment, often in obvious ways, and was motivating other scientists to study the issue and work toward legislation. This was very difficult because the chemical industry was fighting it every step of the way, but they were incredibly successful.
Based on this, I'd really like to understand more about how it was that the environmentalist movement was so organized and potent in this time period. Was it that the problems they were dealing with, like bird deaths, were more obvious? Was it just that we had zero regulation and it was obvious that on the margin, we'd like to have more? Was it that there were actually plenty of good alternatives to things like DDT and CFCs? Is a broken clock right twice a day?
In any case, I have to give a lot of credit to the scientists, popularizers, and politicians who confronted this issue head-on and in a very timely manner. Most of my experience with politics has been one of frustrating impotency, and it's been interesting to review a case where we got it right.
Here's a timeline based entirely on Wikipedia articles and Our World In Data:
I did a little research and this seems to be true, at least if we restrict it to "If we had invented chloroflourocarbons in 1800, and used them as vigorously as we did in real life, we would have severely depleted animal and plant life outside the tropical zone." Our hypothetical air-conditioned Victorians would observe a steady increase in harmful ultraviolet light, spreading from the poles. But the cause would remain a mystery. In our timeline, the ozone layer depletion was discovered by satellite, but could have been detected from the ground if people had been measuring. So we wouldn't have to wait until spaceflight for it to be discovered. But the mechanism by which chloroflurocabons deplete ozone is quite beyond nineteenth century chemistry, and furthermore the ozone layer would not even be discovered until 1913. So they would have kept on using them for many decades. Our fifty years of use depleted the ozone layer over the poles (where it is thickest) by about twofold, but over the equator by only ten percent. In the other time line, it seems reasonable to extend this for 150 years, to a tenfold increase in CFC concentration. This would lead to roughly a ninety percent depletion over the poles and in the temperate zones, and a factor of two over the tropics. This would have catastrophic effects on all life on land or in the shallow ocean. Eventually the economy would collapse and CFC production would decrease, but since it lasts for many decades in the atmosphere, this would not get better for a long time.
Just wanted to say thanks so much to the fact checkers here! It's nice that I was able to update my half-baked thread with your more researched takes. Didn't expect my shower thought to blow up quite so much!