I think
@Polymath257 is trying to provide you some theoretical examples of cosmological models that the universe could be infinite, with Multiverse being one of them.
Other theoretical model of infinite universe is the Cyclical Universe model or the Oscillating Universe model, which is sometimes called the Big Bounce. The cyclical model proposed that the universe goes through alternating series of Big Bang (expansion) and Big Crunch (contraction, back to singularity), sort of like birth, death, rebirth, an endless cycle.
Currently, we don’t have the technology of seeing beyond the surface of last scattering - the oldest observable residual radiation that you would known as the Cosmic Microwave Background Radiation (CMBR). So we cannot see earlier generations of Universe BEFORE this current Big Bang.
Likewise, we have no technology to observe other universes.
Multiverse, Cyclical Universe, and other alternative theoretical models, are only mathematically conceived, not observable, nor testable, at this stage.
Eternal universe is also another theoretical that are not observable, nor testable.
So the questions of universe being infinite or finite, remained an open question, and we really don’t know which one or if any is true.
As to the Big Bang theory, it is a theory about this Observable Universe, stopping the Planck Epoch, with the age of the Observable Universe being 13.79 billion years old, with observable diameter of 93 billion light years.
But I must remind you that these numbers only referred to the “Observable Universe”, but the entire universe, which cannot see, could be much bigger than the known diameter of 93 billion light years.
My point about the Big Bang theory is that it doesn’t attempt to explain anything before and beyond the Planck Epoch.
It would seem that the universe have finite past, according to BB model, but the universe expansion could be infinite, depending on the topology of the universe, eg universe ‘s shape is flat.