https://arxiv.org/abs/hep-th/9402115

and far far away more of them are being created and inflating, once you far enough way you are in something that looks like our universe, somewhere out there inflation is stopping and the big bang is happening there.

It's easy in my mind looking at the classical black hole picture and wondering what happens around the singularity to wonder if inflation gets re-started inside a black hole and maybe in that old picture where you can go into a rotating black hole and come out in the "asymptotically flat spacetime" it is a universe made by that mechanism.

Of course I think the classical black hole picture might be "not even wrong" and you might run into more than one firewall (such as the inflation zone) on the way there.