It's unclear, but there is some evidence that we have, see Early anthropocene - Wikipedia ... also I've an archaelogist friend who talks about the climate impact of European deforestation in the middle ages, but can't find anything online about it right now
Maybe without capitalism we'd have burned the fossil fuels slower, but eventually we'd burn enough of them to get to where we are now under any system (unless maybe the human population is very small?)
I don't think the human population size is an issue either. More so the hoarding of resources by a few of us.