Even before there was a cosmological multiverse, there was discussion about a quantum multiverse which comes from the many-worlds interpretation of quantum mechanics (in the 1950s). It stems fairly naturally from the Schrodinger equation, which for there not to be a quantum multiverse, the Schrodinger equation needs to be incomplete in some way. The problem is that we don’t have any clue how it might be wrong just yet if at all.
There’s also the cosmological multiverse which stems mostly from the theoretical framework of eternal inflation. While we have some positive evidence for inflation in our universe, we don’t have any experimental evidence that this continued on producing other bubble universes. We have tried to think of clever ways to measure other universes but so far have been unsuccessful.
So the multiverse really is just a logical extension of two (or at least one) well substantiated ideas in physics. But of course, it presently lies beyond our ability to measure for the foreseeable future. I’m not sure about the history of it being used in Christian-atheist debates but that’s a little of the background at least as to why it’s a real hypothesis that is talked about in the scientific community.