A wonderful, direct question!
We don't know!
Big Bang cosmology and relativity say that if the universe is infinite, it has no edge to space. If the universe has enough mass to be gravitationally 'closed', then the edge to space is folded around so that it joined back upon itself to form a smooth sphere like the surface of a globe. Astronomers only see and receive information from a small part of the universe we are actually living inside because light has only had about 15 billion years since the Big Bang to do much traveling across the vast space of the present-day universe. We call this the 'visible universe' just to keep in mind that the universe is actually much larger than the part we will ever be able to see. Our visible universe, however, expands at the speed of light, one light years per year, so that billions of years from today, we will be able to se a much larger part of the entire universe that came out of the Big Bang. There is, however, no edge to space like the edge to a piece of paper. At least no theory we know of predicts such a situation!