u would never reach the edge of the universe. there are two reasons why, and both are contradictory.
one: assuming the universe is of the finite, bounded universe, it means that there is no edge, but it is finite. no edge=cant reach it.
two: assuming the universe is of the finite, unbounded universe, it means, somewhere there is an edge. however, to reach the edge, i'll allow ur greater than light spaceship. i'll even allow u to reach close to the edge of the universe. but that's it. u can never go further. why? because the act of being there, means there's 'space' for u to be in. and for 'space' to be there at all, means the edge of the universe just got bigger. u have to be in 'space' for u to exist. therefore, no matter how fast u go, u can never reach the edge.
buuuut, there is another interpretation. if u allow for the existence of another spatial dimension, the fourth spatial dimension, and allow for the possibility of concocting a way to 'fold' urself inbetween 'space' as it is created, then yes, u could reach the edge of the universe. think of it as an analogy: u are a 2-D being with the ability to 'lift' urself into the 3rd dimension by means of 'folding' urself inbetween 2-D space.