Aye, this butts into one of the problems of theoretical physics. Lots of things are possible when we use light speed. If we can travel at light speed we can accomplish all the what ifs. But, it would seem that’s not going to be possible for us in our present format.
Perhaps if we reach a stage that the post-humanists fantasize about and are able to digitize the human mind and upload it to a computer... It would then be possible for the human mind to travel at light speed- as a digitized signal. If it had a receiver at the end of its journey and a computer to install itself in, it would be like sending a program through the air. My modem is wireless...
But there are probably loads of problems with that as well.
For all intents and purposes, we will never make it to the edge of the universe.
But we could never make it to the "edge of the universe," because there isn't one.