On large complex systems, experiment is based on trials and statistics which would require multiple earths. That type of experiment is not possible.
There are fundamental experiments that look at things in isolation. We have done experiments that prove that increasing CO2 concentration increases the amount of heat retained, they take a metal ball heat it up and look at how long it takes to cool with varying CO2 concentrations surrounding the ball. Also, the physics behind CO2's ability to absorb and reemit infrared photons back toward earth is well understood.