So, let me see if I've got this straight? In the beginning, the universe was infinitely dense in an infinite space. That infinite space then expanded, leading to the level of density that we are now familiar with in the universe. But since space is infinite and always has been (even though infinity seems to be getting bigger

), it means that there can be no center to it. Am I grasping the concept so far?
I've certainly never been able to wrap my head around the idea that the universe is really a 2-dimensional or 4-dimensional object and that the 3-dimensional space that we interact with on a day-to-day basis is merely an illusion. It seems to me like Occam's Razor would slice that one to shreds. The fundamental existence of 3-dimensional space as the only space with any practical applications in the universe in which we live seems undeniable.
I suppose, if I'm to interpret the balloon analogy correctly, what you're saying is that, if there is a center to the universe, the center exists in a 4th dimension that cannot be measured and that is the thing that is actually expanding, causing the rest of the universe to become more spread out without changing the actual infinity of it all. Is that right? So that would mean that all matter in the universe, particularly galaxies, is spreading out and away from each other in all directions at equal rates, right?