No. There is probably no way to prove or disprove such a proposition that 'other universes' exist. We are forever precluded from seeing beyond the horizon to our visible universe which all cosmological models predict is only a small part of the complete space-time that emerged from the Big Bang, and by definition is still a part of our universe.
There are two views on this matter. If we strictly define the 'universe' to consist of only those parts of the physical world we can ever have direct knowledge of, this strict definition means that all galaxies that lie beyond the horizon to our current visible universe are not a true part of our universe. Cosmologists prefer another definition of 'universe' based on physics. The Big Bang produced our part of space-time, of which the portion we can currently see is only a fraction of a much larger 'object' created at the Big Bang. In time, we will see more and more of the space in this larger 'object' as the universe continues to expand and light from distant objects continues to arrive at our location in the next billion, 10 billion or trillion years. Cosmologists consider our universe to be that 'largest object' whose totality emerged at the Big Bang, and for which we can in principle eventually observe its entire contents. It may however take billions of years, or even an eternity, for these observations to be completed, but that is of no technical consequence.
Some cosmologists have been bold enough to suggest that in the wondrous depths of some larger space-time, our particular Big Bang may have been only one of an infinitude of similar events, each producing its own separate universe. The problem is that these other universes are more thoroughly cut off from our own than anything we can imagine. Even if our universe is destined to expand for all eternity, it will never encounter any of these other space-times. There is therefore no conceivable observation we could carry out within our own universe that could lead us to observe any of these other universes. This means that, without any hope of observational confirmation, these proposals are dangerously close to not being scientific. "If you can't test it, it ain't science!"