I believe our universe is not unique. As science has evolved, our place within the universe has continued to diminish in significance.
First it was felt that the Earth was the center of the universe, then that our Sun was the center, and so on. Ultimately we now realize that we are located at the edge of a random galaxy that is itself located nowhere special in a large, potentially infinite universe full of other galaxies. Moreover, we now know that even the stars and visible galaxies themselves are but an insignificant bit of visible pollution in a universe that is otherwise dominated by 'stuff' that doesn't shine.
Dark matter dominates the masses of galaxies and clusters by a factor of 10 compared to normal matter. And now we have discovered that even matter itself is almost insignificant. Instead empty space itself contains more than twice as much energy as that associated with all matter, including dark matter, in the universe. Further, as we ponder the origin of our universe, and the nature of the strange dark energy that dominates it, every plausible theory that I know of suggests that the Big Bang that created our visible universe was not unique. There are likely to be a large, and possibly infinite number of other universes out there, some of which may be experiencing Big Bangs at the current moment, and some of which may have already collapsed inward into Big Crunches. From a philosophical perspective this may be satisfying to some, who find a universe with a definite beginning but no definite end dissatisfying. In this case, in the 'metaverse', or 'multiverse' things may seem much more uniform in time.
At every instant there may be many universes being born, and others dying. But philosophy aside, the existence of many different causally disconnected universes—regions with which we will never ever be able to have direct communication, and thus which will forever be out of reach of direct empirical verification—may have significant impacts on our understanding of our own universe. Their existence may help explain why our own universe has certain otherwise unexpected features, because in a metaverse with a possibly infinite number of different universes, which may themselves vary in their fundamental features, it could be that life like our own would evolve in only universes with a special set of characteristics.
Whether or not this anthropic type of argument is necessary to understand our universe—and I personally hope it isn't—I nevertheless find it satisfying to think that it is likely that not only are we not located in a particularly special place in our universe, but that our universe itself may be relatively insignificant on a larger cosmic scale. It represents perhaps the ultimate Copernican Revolution.