There are pretty compelling arguments for a multiverse and indications that our universe could be part of it. There's no evidence that cannot be interpreted to mean that there are no other options though.

In my opinion, the various multiverse concepts are not falsifiable and cannot be advanced as theory. Someday we may have the technology though.

Before Stephen Hawking died he published on eternal inflation.
Abstract: The usual theory of inflation breaks down in eternal inflation. We derive a dual description of eternal inflation in terms of a deformed Euclidean CFT located at the threshold of eternal inflation. The partition function gives the amplitude of different ge- ometries of the threshold surface in the no-boundary state. Its local and global behavior in dual toy models shows that the amplitude is low for surfaces which are not nearly con- formal to the round three-sphere and essentially zero for surfaces with negative curvature. Based on this we conjecture that the exit from eternal inflation does not produce an infinite fractal-like multiverse, but is finite and reasonably smooth.

here is the link: [link.springer.com]

How much proof do you really need?