Put a Clovis point on an atlatl dart. Fill the fluted grooves with aconite poison from Monk's Hood roots (for example). Launch that missle at a herd of megafauna from 100 yards away. BBQ mammoth will be on the menu for the next week. The animals that became extinct were herd animals that were easy to kill with weapons such as the atlatl. While the herds lasted, it was an easy way to make a living.
One of the neat things about a bow is that you can shoot it pretty inconspicuously. To use an atlatl on the other hand, you've got to pretty much make a flaming spectacle of yourself. A mammoth elephant would pick up on that and stomp you flat.