My understanding was that there appears to have been an extensive network of villages ( not large population centers though) that ran from the foothills of the Andes to the coasts that used 'roads' and of course river travel. I remember that upon later research that it was posited that the primitive almost Stone Age cultural level of the modern indigenous peoples in the Amazon is a reflection of the destruction of that more culturally advanced village network civilization. I also remember that the Inca were trade partners of sorts with the Amazonian culture. I do not remember the high population figures of tens of millions that you cite!
It is very likely ( at least to my reasoning ) that similar 'primitive' cultural/trade networks existed during the pre Bronze Age eras in Europe and Asia. When the more advanced technology (Bronze) cultures encountered the Stone Age technology cultures, the disparity of technological advantages encouraged attempts at conquest. It wouldn't be the first nor the last time that disparate technologies resulted in the destruction of the more primitive. So it is possible that the modern Stone Age Amazonian tribes are the descendants of a more advanced but now destroyed cultural/trade tradition.
However the issue that I was debating was the erroneous notion that greater tree cover encourages global warming.