Aside if you tell me that burning oil is far more polluting than burning wood that's another story, but in formal CO₂ terms...
- US, China, and UK emissions per capita since 1751: https://www.researchgate.net/figure/Historical-CO2-per-capit... (data: https://data.ess-dive.lbl.gov/view/doi:10.3334/CDIAC/00001_V... )
This is unsurprising - though heating and cooking require a significant amount of energy even in the modern day, they only account for 23% of global energy usage (https://www.iea.org/reports/renewables-2019/heat). The largest energy user is transportation (35%) followed by manufacturing (20%) (https://www.iea.org/data-and-statistics/charts/largest-end-u...), neither of which were probably much of a factor in the pre-industrial world.
First, burning wood is carbon neutral. The tree pulled it from the air and burning returns to the air.
Second, there are natural processes that absorb carbon and keep system in a balance. Trees are one, plankton is another, and longer term is rock weathering. Even if the ancestor were using coal, the absorption processes could keep up with the small amount.
Coal and gas are millions of years old.
We wouldn't have a problem of we only burnt wood for energy, but we wouldn't have our modern society either.