I doubt this. Population levels and population density levels of ice age hunter gather people were never high enough at the time to cause a mass extinction world wide, nor did they have adequate weapons to do so.
Consider the case of the Plains Indians and the Buffalo herds. The herds grew to huge proportions but the Indians never had populations high enough to put a dent in the population.
We have a country of 300 million people , many of whom hunt and we have a hard time keeping the deer population down
Those animals have fairly high reproductive rates. Some of the large animals produce few young, and it takes a long time for the young to mature to reproductive age. Elephants, for example, gestate for two years and become sexually mature at age 14. Some of the megafauna (which were much larger than elephants) probably had even longer cycles. With such a slow reproductive rate, it would not take much hunting to disrupt the viability of the herd. Couple that with the climate changes--large body mass makes dissipating heat difficult--and they could not survive.
They were using extremely powerful assault spears with high capacity clips filled with extremely powerful “FLINT” spear points which are specifically designed to kill megafauna.