Did cro magnons and native americans hunt european cave lions nd american lions to extinction?
No. The North America version didn't go extinct; the tigers did but it wasn't from hunting. The European cave lions stuck around until Roman times.
That, and the larger wildlife the two species consumed were wiped out when the glaciers retreated and their food supplies shifted (for the herbivores). We lost the North American Hyena, the Cheetah (it was twice the size of the African Cheetah), the North American Leopard, the Dire Wolf, the Cave bear, the Short Faced Bear and any scimitar toothed cat as well.
Probably. ... but then we have to wonder why grizzly bears and cougars did NOT go extinct. It's puzzling.
Most likely yes. The Holocene extinction includes the disappearance of large land animals known as megafauna, starting at the end of the last Ice Age. Megafauna outside of the African continent, which did not evolve alongside humans, proved highly sensitive to the introduction of new predation, and many died out shortly after early humans began spreading and hunting across the Earth.