The the surface of the earth has temperature X. We can measure measure X with some degree of precision.

Any theory of physics that makes a prediction about the earth's temperature can be checked against the measured value of X.

All widely accepted theories that predict a temperature near X rely on the role of greenhouse gases and CO2 in particular to yield that temperature. And they all agree, more or less, that every doubling of the atmospheric CO2 concentration will result in an equal additive increase in our equilibrium temperature (so equilibrium temp grows as the log of the CO2 content).

Granted, to make _very precise_ predictions, you need to add forcing factors and feedback mechanisms that are hard to measure and hard to model and that's where computer simulations run into trouble. But the theory is sound and widely accepted.

I got most of the above a few years ago from some version of this class: https://www.coursera.org/learn/global-warming

Also the instructor's book, and the IPCC report from a few years ago.