There is no edge to the universe, any more than there’s an edge to the Earth.
If we imagine a small universe, what happens is you sail farther and farther away from Earth, and eventually you see a sun in front of you and orbiting that sun is Earth.
Except in our universe, even if our universe turns out to be finite and curved, you’d never be able to actually do this because even travelling at 99.99% of the speed of light you’d never reach the antipode–the antipode is receding away from you faster than the speed of light.
Imagine trying to sail around the earth, but the earth is expanding faster than your ship can sail. You’ll never get back to your home harbor because the ocean keeps getting bigger.
It could have been that we lived in a universe that was small enough that it would be possible to travel back to your starting point by going away far enough. Or to put it another way, we could train our telescopes out into distant space, and see a very faint galaxy and recognize it as our own milky way, except in the distant past. But we don’t live in such a small universe, light from the early milky way can never travel all the way around the universe and back to our telescopes because the universe is too large, and is expanding fast enough that the light from that early milky way isn’t closer to us every day, it’s farther away from us every day and therefore will never reach us.
This is assuming we’re talking about a spaceship that can travel Nearly As Fast As Light. If you’re asking about a spaceship that can travel Faster Than Light, who knows what would happen, because if FTL travel is possible in our universe then our current understanding of the universe is seriously flawed.