Then it warmed the surface.
Which warmed the atmosphere.
The heat (infrared radiation) bounced around between CO2 and other air molecules through most of the atmosphere where it is optically thick (opaque to IR).
Eventually it got to a height where CO2 molecules are far enough apart for the atmosphere to be optically thin and you can see space in IR.
Then it shot off into space as IR radiation.
The CO2 we've added makes that height higher and colder so the emitted IR carries away less energy.
The Sun hasn't got colder so same energy in minus less energy out = positive energy balance = warming. Simple arithmetic.
When we've warmed up enough for the higher radiating height to be as warm as the old, lower radiating height we'll stabilise at a new, higher temperature.
Of course if we keep adding CO2 we'll never stabilise.