As the last habitable continent colonized by humans, the site of multiple domestication hotspots, and the location of the largest Pleistocene megafaunal extinction, South America is central to human prehistory. Yet remarkably little is known about human population dynamics during colonization, subsequent expansions, and domestication. Here we reconstruct the spatiotemporal patterns of human population growth in South America using a newly aggregated database of 1,147 archaeological sites and 5,464 calibrated radiocarbon dates spanning fourteen thousand to two thousand years ago (ka). We demonstrate that, rather than a steady exponential expansion, the demographic history of South Americans is characterized by two distinct phases. First, humans spread rapidly throughout the continent, but remained at low population sizes for 8,000 years, including a 4,000-year period of 'boom-and-bust' oscillations with no net growth. Supplementation of hunting with domesticated crops and animals had a minimal impact on population carrying capacity. Only with widespread sedentism, beginning ~5 ka, did a second demographic phase begin, with evidence for exponential population growth in cultural hotspots, characteristic of the Neolithic transition worldwide. The unique extent of humanity's ability to modify its environment to markedly increase carrying capacity in South America is therefore an unexpectedly recent phenomenon.