if I wanted to travel to the edge of our universe which direction is the shortest route?
Linearly there is no shortest route. Distance in every direction is the same. No matter which way you look, you can see the universe as it was about 13.8 billion years ago. How can that possibly be true?
With the Big Bang, our universe expanded into existence but it was not like an explosion you watch in a quarry. If we detonated a large bomb in outer space you would see a detonation that expands out in all directions. But what if the space around every particle from that explosion, itself expanded out in all directions? And every piece of space from that expanded out in every direction?
Space (actually space-time because the two are connected) expands in every direction from around every particle. Raisins in a loaf of raisin bread expand away from every other raisin. This is a popular way to demonstrate this. Of course the loaf is contained in a bread pan, but in reality, in our universe, there is nothing to contain it except the forces generated within it- those of magnetism and gravity and the expansive force we call dark energy.
So imagine sitting on a raisin next to a clump of other raisins. As the loaf expands every raisin you can see expands away and gets farther and farther from you. If you were on a different raisin, you would observe the same thing. Raisins below you expand away. Raisins above you expand away. Raisins anywhere expand away. If the raisin bread continued and continued to grow eventually the raisins would be very far away. That is what many scientists predict for the end of our universe in 40 trillion years or so. We will be all alone and eventually the space within our own atoms will expand away. Though we wouldn’t survive it, we’d all have to be there of course to see that.
All of the material we see- other galaxies- planets in our solar system, our sun, our Milky Way Galaxy are all moving. Some might be moving through space toward us, but the space through which they are moving is getting larger.
Currently things might be moving toward us at a rate faster than space is expanding. That is why the Andromeda Galaxy will, in about 4 billion years, collide with our Milky Way Galaxy.
Something that far away in time is purely academic of course but it does appear to be happening.