You’re correct. The last ice age was melting down around 13,000 years ago and then the Younger Dryas ‘occured’. A new theory, with strong supporting evidence suggests an asteroid or comet impact in the Eastern Canadian ice sheet caused the Younger Dryas, the mass extintions of large animals in North America and the end of the Clovis culture. The animals had survived many ice ages before so renewed glaciation would not have posed a threat. Their abrubt extinction at the same time as the Clovis people as well as the rapid return of glaciation point to catastrophism.
That makes sense. I can also imagine that animals that had adapted gradually to warming over a few centuries might have been socked pretty hard by an abrupt shift to cold no matter what caused it.