It doesn’t expand into anything. It has no edge. It expands within itself, like it’s distorting itself. Alternatively, you can picture it as groups of gravitationally bound objects (= galaxy clusters) moving away from each other everywhere in the universe. It’s a bit like raisins in a cake being carried away from each other by the dough expanding in the oven. Where the cake already fills all space infinitely in all directions, from the very start. Space is the cake dough. There is no “outer” space that space expands into. The geometry of space itself expands.

Still alternatively, imagine an infinitely extended graph paper whose grid size slowly and continuously increases, carrying with it the dots already drawn on it. Since the grid has infinite size from the start, it doesn’t expand into anything. It just expands.