Final answer:
Humans could have interacted with mammoths during the late Pleistocene epoch, specifically in the time span of 10,000 to 4,000 years ago when mammoths went extinct due to factors like over-hunting and climate change.
Step-by-step explanation:
The period during which humans could have potentially interacted with mammoths, including activities such as hunting or the humorous notion of 'pulling the mammoth's tail and running,' is known as the late Pleistocene epoch. This was the time of the Pleistocene Extinction, which is the geological time span during which mammoths began to go extinct, around 10,000 to 4,000 years ago. Woolly mammoths managed to survive on Wrangel Island until about 1700 BC. The extinction of mammoths was likely due to a combination of factors, including human over-hunting, climate change, habitat reduction, and human migration across the Bering Strait. Archaeological evidence shows that humans hunted large animals like woolly mammoths, indicating that as homo sapiens expanded, they had significant impacts on the megafauna they encountered.