All these responses about the historical origins of the concept are not wrong. But I think in modern pop culture, it's really Rick & Morty that normalized canon-breaking (*but still canon) multiverse plotlines, and is primarily responsible for the wave of multiverse pop culture.
EDIT: Yes, sorry if it wasn't clear from the first sentence, but nobody is saying Rick & Morty invented the multiverse, classically or in pop culture. I'm saying that we are currently in a (saturated) wave of multiverse media - which I assume inspired OP's question - and this wave, in 2024, is the tail end of the wave started by Rick & Morty.
Right, I mean, I'm not saying it's a new idea. Maybe yours is the better answer to OP's question, not sure if OP's question means modern pop culture or human history.
There was the idea of the multiverse on television well before Rick and Morty.
You have several instances in Star Trek, including the Mirror Universe in TOS. "Mirror, Mirror" aired in 1967 and was one of the first instances of evil versions of people having goatees.
The show Sliders has a portal device and the show is centered around taking portal trips across the multiverse. That started airing in 1995.
Rick and Morty has used a lot of these tropes to make interesting shows, but they are more recycling old ideas in new ways than making new ones from scratch.