Homo sapien expansion after the last glacial maximum is a strong contender, but my understanding is that we don't yet have enough data to rule out environmental changes, or sufficient resolution to really prove it was us.

The most convincing argument I've heard points out that Africa - where we evolved - has more surviving mega-fauna than any other continent. If animals who had more evolutionary time to develop strategies for coping with humans are way more likely to survive, that strongly suggests we played a large role.

It's an area of ongoing research without a definitive answer though.

Not only had they previously been here, they evolved here first and migrated out through Siberia when it still connected the continents.

The interesting part is that they evolved in America, crossed over to Asia (and from there to Europe and Africa) through the Bering land bridge, and then went extinct in America together with the American megafauna (possibly because of overexploitation by recently arrived humans, possibly due to climate change, possibly a combination of both), only to be reintroduced later on.

The usual reason, probably.