The universe isn't expanding "into" anything, it's expanding out from itself. I imagine that makes no sense, so I'll try to explain better. We have the misconception of the universe being like a balloon, where the expansion is like air filling it and pushing the edge out. But there is no edge to the universe, and space is expanding everywhere at the same time, not just from one point. When you think of the expansion of space, you think of let's say two galaxies moving apart from each other, but it's not like two cars driving apart from each other. The actual space between them is growing, so it'd be like if the cars didn't move themselves, but a road was built between them that increased the distance between them. So every galaxy is moving away from every other galaxy at the same time.