First, this thought experiment uses the conditions that the universe undergoes decelerating expansion and then contraction, as is the Big Crunch theory. **I know this is contrary to current evidence, supernovae surveys etc., but the thought experiment assumes a closed universe which will have a Big Crunch scenario as one of its conditions. As the universe undergoes contraction, the super-clusters lump up and galaxies pile closer. So, more super-clusters of galaxies clump together. Imagine there are eventually 3 (or some other small number) of major chunks. You could imagine their centers have ulta-massive black holes which are in the range of billions of galaxies in mass. So, we have 3 major centers of mass now at this near-end stage of the Big Crunch. At this point we can easily see that there is a geometrical center between them, and as they are all that comprise the universe at that time, that center is the center of the universe. It would be uncertain if there could have been no center until nearing the end, but one would have to assume that if there can be a center at the end, then there must have been a center throughout the existence. Again, try to take the grounds of the Big Crunch and ignore dark energy.