An accurate analogy would be the dough/raisin analogy that’s commonly used: the universe is a blob of dough with raisins spread throughout it. When you put the dough into an oven, the dough expands, taking the “stationary” raisins with it, increasing the distance (space) between the raisins.
Without any way to leave our little raisin, there is no way to see the “end” of the dough – so, if we assume that the universe is truly infinite, then it simply doesn’t have anything to “expand” into. Using a mathematical analogy, you have a series of whole integers that start with one to infinity. If you took every number and multiplied by any factor, the numbers in your series have stretched away from each other; yet the list hasn’t expanded. You still have a series that progresses from a number to infinity.