You're asking about something that's beyond the realm of well-understood physics, so a lot of it is speculation. However, people work on the idea, so it's not impossible. The key words you want to look for are eternal inflation and multiverse.
The gist is that in our universe, shortly after the Big Bang, there was a phase where the universe expanded at an exponential rate (known as "inflation").* It turns out that one way to model inflation is that the true universe is always inflating, and our universe is just a bubble within that eternally-inflating universe. Eternal inflation has some fun consequences, e.g. if it's true, then there are multiple universes out there each with their own Big Bang and laws of physics. The universe is probably not stable as a result (but don't start buying insurance, because if the universe really is not stable, then when the false vacuum decay happens, the insurance company will also cease to exist).
If eternal inflation turns out to be true, then the answer to your question is 'yes'. The problem of course is that eternal inflation itself is a speculative model which is very far from being experimentally verified. Some people even argue it's not science since it doesn't make verifiable predictions. Other people think it's still worth working on, because if string theory turns out to be true, then string theory could naturally lead to eternal inflation. People who take this view argue that in the same way that we trust General Relativity to predict what happens inside black holes (even though we cannot observe that directly), we should also trust eternal inflation if it's predicted by string theory. Yet other people pour cold water on that, since in this picture we are one of the estimated $10^{500}$ universes that is predicted in string theory, and if there actually are $10^{500}$ universes then almost anything is possible and the theory loses predictive power (this number is many hundreds of orders of magnitude larger than the number of atoms in the observable universe).
Finally, if your question is not whether it happened but whether it's plausible, then the question is unambiguously 'yes', since eternal inflation hasn't been rejected yet - but again, we are talking about things that's beyond the realm of well-understood physics, and a lot of it is speculation.
*It's worth pointing out that there's no compelling evidence for inflation yet. Many cosmologists believe it's true, but the evidence is not at the level where it is compelling.