The entire universe is infinitely large, (we think) but the observable universe is finite, limited by the age of the universe, the speed of light, and the portion of the early universe when space was opaque. (which is what the cosmic microwave background, or CMB is) (note that terminology is confusing; when people use the word "universe" you have to determine base on context whether they're talking about the infinite entire universe, or the finite observable universe)
Imagine an RTS game on an infinitely large map with fog of war. Sure, there's something out there beyond the fog of war, but we can't see it. (don't try to go too far with this analogy though)
The universe isn't expanding into anything. It just is. This is the key to your misunderstanding I think; the universe isn't expanding through or into some other, extra-dimensional medium. The universe itself is expanding.
Imagine an RTS game on an infinitely large map with fog of war. Sure, there's something out there beyond the fog of war, but we can't see it. (don't try to go too far with this analogy though)
The universe isn't expanding into anything. It just is. This is the key to your misunderstanding I think; the universe isn't expanding through or into some other, extra-dimensional medium. The universe itself is expanding.