Because they didn’t actually live in caves that often.
The image of these people living in caves arises from the fact that caves are where the preponderance of artifacts have been found from European Stone Age cultures. However, this most likely reflects the degree of preservation that caves provide over the millennia, rather than an indication of them being a typical form of shelter. Until the last glacial period, the great majority of humans did not live in caves, as nomadic hunter-gatherer tribes lived in a variety of temporary structures, such as tents[4] and wooden huts (e.g., at Ohalo). A few genuine cave dwellings did exist, however, such as at Mount Carmel in Israel.>
China accounts for 30% of global emissions and, granted the states is half that, but they are still number 2. Also, the per capita number suggest that it would be easier for the individual to make a difference in the states.
Arguably a lot of China’s emissions come from industry. As America has outsourced a lot of it’s Industry to places like China these emission stats are probably somewhat warped.
https://www.worldometers.info/co2-emissions/co2-emissions-by-country