Ice ages occur every 50-100KA, both the mammoth and the sabre toothed tiger evolved around 2.5MA ago and survived the end of dozens of ice ages before going ext

Ice ages occur every 50-100KA, both the mammoth and the sabre toothed tiger evolved around 2.5MA ago and survived the end of dozens of ice ages before going extinct during the end of the last one, just as humans showed up. This pattern holds for numerous other megafauna species. If humans had nothing to do with it, why didn't previous ice ages make them go extinct?