Not clear how many mammoths in a herd - but the math of female maturity & reproduction vs. hunting and climate should be considered also.
A female mammoth reaches maturity at 15 with a gestation period of 22 months. Not clear on life expectancy - but if hunters killed off pregnant females (or in estrus) and/or their young...that could have caused a severe repopulation problem.
I just think too much was going on to blame humans for the mammoths. Too many other species (dire wolves, saber-toothed cats, cave bears, giant bison, North American camels and horses, etc.) died out at the same time.
There is a natural sort of husbandry involved in the hunter-gatherer lifestyle - Game becomes scarce long before any regional extinction level - The economy of successful hunts depends upon flourishing herds. When the fishing gets bad because of over-fishing, when herds diminish and get spooky because of over-hunting, when resources diminish to a point of difficulty (wood for fire as an example), a Hunter-Gatherer culture begins to starve, and is forced to move on.
As a general principle, this can be seen in native tribes, that would often travel great distances between summer and winter habitation. It is the advent of farming - a food source not tied to the natural economy of the land - and the eventual construction of cities, that made (make) humans capable of extinction level hunting.