Astronomer here! The universe isn’t expanding into anything. I think the reason a lot of people have trouble with this is a lot of analogies rely on a smaller 3D object expanding (like raisin bread in an oven that is baking, and the galaxies are like raisins in the loaf going away from each other- true but gives the wrong impression as a whole).

Instead, I think it’s easier to grasp if you imagine a number line: 1, 2, 3, …, infinity. Now let’s double the numbers in it: 2, 4, 6, …, infinity. You have made the values in your number line twice as big, but it still has the same number of numbers! That is what the expansion of the universe is like- not expanding into anything, just the thing itself is growing.

Hope that helps!