Keith - I agree that other factors were probably involved, like species ranges reduced by ice, making small populations more vulnerable. But big mammals breed very slowly, and people no doubt acted like other predators and focused on the babies - much safer. It takes a couple of hunters to distract mom while another kills the kid - lions hyenas, killer whales, and wolves use this tactic, and highly efficient human hunters with dogs could have had much of their impact this way. We probably also wiped out whole herds at a time, like the buffalo jumps in the west. Once favored prey species were seriously reduced by man, predators may then have turned to smaller prey, further impacting those species.
I would not assume that human numbers remained low very long - humans found two whole continents full of naive prey and could have increased in number and range rapidly due to abundant food. Fascinating to speculate about, and our generation is witnessing the end stages of the process.
