Shortly after the Civil War. All Atmospheric Scientists/Meteorologists are taught this in their radiative transfer courses.
The extent of climate change possibilities started being tested in the 1970s using primitive equation models with the first really sophisticated computational machines. Actually I think the first pre-computer attempt using math students doing it by hand a century before or more. The models became more sophisticated by the 1970s as weather forecasts from these models became better than the empirical rules taught to meteorologists and other weather forecasters.
By the late 1970s and early 1980s scientists were beginning to use these models for trying to gauge climates in earth's past and trying to match them with the fossil record. This attracted the attention of the oil industry. Certain depositional environments were responsible for generating oil and gas bearing formations. The utility of climate models was quickly realized and became a closely guarded secret, at least until the leasing rights were secured.
Climate modeling really reenforced the impact of CO2 and other greenhouse gas levels in the Earth's past. The first climate models assumed current greenhouse gas levels for ancient climates where the fossil record indicated much higher global temperatures. The only way to make the climate models match the fossil records was to increase CO2 levels until modeled temperatures matched what the fossil record said. The definitive collaboration that global temperatures were tied to CO2 and other greenhouse gas levels came from the Greenland and Antarctic ice cores, which showed a definitive link between temperature and CO2 levels. This was the first instance when atmospheric composition could be directly measured over time and be compared with waxing and waning ice sheet levels (and global temperatures).
What most people miss is the science of climate change has been worked out for over a century. And paradoxically, the fossil fuel industry was a big supporter of the science developed over the last 50 years that yielded the details of how climate has responded to different greenhouse gas levels in the past.
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