You're assuming that natural cycles and increased CO2 have some sort of connection in this case. We're talking about CO2 of an origin not seen before in earth's history, so strict reliance on what happened in the past isn't valid. The whole point is to find out how much natural cycles are being altered by increases in absorbed energy due to added CO2. Other instances of warmimg and cooling in the past may be interesting as natural huistory, but aren't a template for our time, because of changes in underlying conditions.
So, when the CO2 levels were orders of magnitued higher then they are now....how did they get that way?
There could be all sorts of reasons, e.g. volcanism, but since I'm more concerned about what's happening NOW and determining THOSE reasons, I really don't have time to do your natural history homework for you.
Volcanoes are a pretty weak source of CO2. A great one for Sulfur, however.
Sulfur actually works against the GH Effect.
The question, though, relates not to a specific source but rather to a specific non-source. When CO2 was higher in the past, Man was NOT the source.