Not that long gone—the last relict population on Wrangel Island only died out about 4000 years ago. That’s (barely) within historic time. There are probably islands in the Canadian and Siberian Arctic that could still support them (and have no or few human inhabitants).
I see two big issues. First of all, not all knowledge among elephants is transmitted genetically, and I expect mammoths were the same. Who will the new ones learn from? They’ll have to redevelop best practices for dealing with their environment from scratch.
Secondly, global warming. This seems like about the worst possible time to bring back an ice-age-adapted critter. We’d be better off transferring the effort spent on this project into de-extincting the thylacine, a more recent loss which doesn’t have that specific issue.