We have no idea, and we can't know apart from divine revelation, if our universe is the only one. The implications, however, indicate that this universe is the only universe.
Nothing in Scripture talks about multiple universes. It seems unnecessary for God to have made multiple universes (what purpose would it serve?), and I feel it would be dishonest for God to make another universe without telling us about it. God doesn't need to tell us everything He's doing, far from it, but I feel it would be dishonest.
Scripture claims there is no god like God (Ps 86:8, 1 Chr 17:20, 1 Ki 8:23, etc). I understand a god to be anything that is worshipped as most important. In that sense that are millions and even billions of gods. But as far as an entity that is wholly independent of everything else (which is what "I am that I am" means, in addition to other things), there is only 1 according to Scripture.