According to John Barrow's book "The Infinite Book", there are several different 'types' of infinity, and each & every one just as inaccessable to the human mind as percieving four spatial dimensions.
Scientists have been struggling to glimpse to the known edges of our visible universe, and noticed that galaxies seem more 'condensed' the further they look. This is due to light from billions of years ago finally reaching us. Obviously, the galaxies themselves have moved on since emitting that light, but it gives scientists a rough idea of when the big bang occurred, and how 'big' the universe is at the moment.
However space is not just a big balloon that keeps blowing up to even bigger size. That is merely thinking in 3 spatial dimensions, while scientists have discovered that there are at least 10 spatial dimensions in the universe. Einstein has suggested that the universe is fabricated as spacetime, and as matter travels faster (& therefore gets heavier), it warps the space, & light around it. Due to these factors, discovering a physical 'edge' to the universe, like a wall of plasma, or a fence with a sign saying 'nothing beyond this point' is not very likely.
When early explorers started exploring the world, maps would usually have something like 'Here be monsters' in unexplored areas. In the heavens, humans imagined a celestial sphere, a black bubble with dots of light for the stars, that contained the sun, the moon and the earth, with everything else painted on its ceiling. Outside the bubble was heaven.
Obviously, we know that these theories are not true, but we're still doing the same with what is 'beyond' space. We're struggling with concepts such as 'borders', because we don't know & can't see any. We're struggling with the concept of absolute nothing, because even in a vacuum, there are still particles. We're stuck in a 3 dimensional world-view, and unable to count to infinity, because it is always one more number away from the one we can count.
It's great to contemplate the infinite universe, but I don't think the human mind can ever really 'see' it or imagine it. Still good fun trying, but don't try it after smoking anything! ;-)