cosmology - Is parallel universe possible

As much as parallel universes go, there's a theory for this known as the Multiverse theory, part of the String theory.

In String theory, the Multiverse is a theory in which our universe is
not the only one; many universes exist parallel to each other. These
distinct universes within the multiverse theory are called parallel
universes.

There are cosmic inflation models that support this as said here in Wikipedia. A quote from there:

It's hard to build models of inflation that don't lead to a
multiverse. It's not impossible, so I think there's still certainly
research that needs to be done. But most models of inflation do lead
to a multiverse, and evidence for inflation will be pushing us in the
direction of taking [the idea of a] multiverse seriously. Alan Guth[7]

Now to address your point if we can ever know if a parallel universe exists exists.

Opinion: Possible but unlikely. I don't think that we are close to achieving this.