Since everyone agrees that the earth is warming, then we only have to look at possible sources.
Because the earth is a ball in space, the basic thermodynamics of it are quite simple. A certain amount of light falls on the earth, a certain amount is reflected back and the rest is absorbed and re-radiated out (eventually).
CO2 is a greenhouse gas, basic physics. Without the amount we have the average temperature on earth would be far lower. Ask Venus how things are going with its CO2.
One can then analyze the concentrations of various isotopes of CO2 in the atmosphere to see where they came from. The CO2 released from burning fossil fuels has different ratio of certain isotopes compared to other sources.
So if you do that analysis on the current CO2 in the atmosphere, and compare that to historical CO2 in this the Holocene epoch, you get a certain result of so much regular CO2, and so much CO2 from burned fossil fuels.
And if that extra amount lines up with the expected temperature increase, well you'll just have to read the story to see the end
I mean it's really basic. Take billions of years worth of CO2 locked up in dead plants and animals, then release a significant portion of it in 1 millionth the time it took to make it. If I put all the garbage I've thrown out over 20 years and brought it back into my house for 1 second, that would have an impact on my house.