There is no evidence the mammoths went in one big blast or any impact caused any long term or global impact.
All these big animals went extinct over an extended period of time. What shows man did it was the last remaining populations of these animals were in the remote areas where man was last to show up.
So either man did it or by an amazing coincidence where ever man showed up the climate changed and a comet hit.
That gives us 19 interglacials (10,000 years or longer) and an unknown number of interstadials (shorter than 10,000 years).
Mankind was present for at least four of the interglacials and many of the interstadials. The Mastadons thrived. The tigers thrived!
This latest situation, the Younger Dryass, was unique ~ the other periods of glaciation did not not stop and start up right away. They just stopped.
We are still in an ice age. But there are a lot fewer big cats around to stop our advances. Humans didn't kill off the cats ~ hunger killed them!
No, in fact, they did not. That peculiarity has been the reason so many have been looking for a cause for so many years, and why the blame has been put on mythical, nearly superhuman hunters.