Yes, CO2 levels have varied in the past. There is some data to suggest it can be a following parameter, e.g., that it rises after a rise in T caused by cycles or whatever.
The steady rise of CO2 in the air coupled with the isotopic data strongly suggested this is mostly due to fossil fuels being burned. We have a reasonable handle on how much CO2 is produced each year from FFs and the levels match up up fairly well.
We obviously do burn a LOT of FFs each year. A gallon of gasoline generates a surprising (to me) amount of CO2 (because the O2 part is so heavy).
I don't fully trust the models though, they can only be devised by "back fitting". There may be a lot of important parameters not being considered.