We know for a fact that CO2 slows the radiation of heat. We can measure in a tube the precise degree to which it slows the radiation of infrared, and in a tube that traps gasses physically, we know that slowing the radiation of infrared further traps heat.
Quantum Mechanics tells us this is true. We can precisely calculate the probability that a CO2 molecule will catch an infrared photon, and we have testable and, BTW, spectacularly well tested theories, that show that after a time, the molecule will either re-radiate the photon in some arbitrary direction, including down in the case of the atmosphere, or collide with another molecule, passing its heat on that way.
We also know that a body which is absorbing heat must radiate that heat in equal measure or it will warm. Slow the radiation of heat and the body will warm. Nobody disputes this. We just don’t know anything right now about how the effects of a CO2 molecule, or any other molecule that can absorb infrared, shake out in a system as complex as that of our planet.
If one has an air cooled gasoline engine, one can’t just calculate that it will overheat or not based on the properties of the metals it is made of and the gasoline it burns, one must also take into account the configuration of that metal. Does it have cooling fins? That is a big part of the answer. In the case of the planet, it may be that the configuration of any “cooling fins” and their effectiveness is not readily apparent and that the sum of any heating and cooling effects caused by CO2 is not a tractable calculation, even if we had the measurements.
What can we do in a case like this? We can only measure the effect and infer the rate of warming caused by GHG based on measurements. This is not perfect because it is likely that climate effects such as ocean currents and oscillations, changes in biology, ice extent and volume changes, cloud cover variations, etc… are causing a kind of climactic Brownian Motion, hiding the signal in what, lacking deep understanding of these issues, we can only call noise.
That is where we are. We have an undoubted effect, but we can’t measure it except in the crudest manner. That is why the pause is as important as the jump in temperatures that preceded it. We can’t pretend that we “just know” that heat is building on the planet if we can’t see the planet heating on the grounds that “it must be somewhere” because it doesn’t have to be anywhere on the planet, it may be radiating away, light years away, in the case of the pause.