Modern scientific cosmology has been unable to determine whether or not the Universe is infinite. This is no failing of the ever-refining iterative investigation which is science and – for all that science, physics and mathematics has taught us, it may be of the essential nature of the mathematical incomprehensibility of infinity that we might never ever be able to fully prove (beyond educated conjecture and logical assertion) the finite or non-finite parameters of our Cosmic container and ultimate context. There may be some probabilities which are more likely than others, and some which are relatively self-evident from experimental results and the fruits of hypothesis and theory.
A curious consideration: if we live in an infinite Universe, it is a matter of mathematical fact that anything that can happen, will happen and will happen an infinite number of times. All possibilities would happen, all possible configurations of matter and energy including you, repeated infinitely many times, every single possible variation and all possible histories. For this reason I suspect it is foolhardy to proclaim anything “impossible” and not just because of our extremely limited survey of reality and our limited lifespans, comprehension or effect in the Universe. The issue strikes me more as: even if the Universe is not infinite, the sheer staggering statistical inevitability of almost every possible configuration of matter, energy, life and intelligence across the trillions of galaxies would have to imply that we, like Jon Snow, really do know nothing.