As far as I’ve heard, there’s no specific coordinates in the Tanach about where the temple must sit. Indeed, Herod’s temple was hardly akin to the first temple in exact location or building specifications.
On the simplest level, so much of Judaism is innaccessible without a temple. From korbans to the Sanhadrin. So if we can’t get exactly on top of the hill, why not rebuild it right next door, in the Western Wall plaza, or even the car park beyond the gate and have a pipe connecting the old temple to the new one. The Kotel can still be an outer wall for the new one. We can lift up the rocks scattered around, even build it at the same height and simply increase the size of the hill, which Herod did anyway when he made his extensions, and likely the builders of the second temple did as well.
Halachly, is it not more important to restablish a physical building and “re-start” Judaism than to keep on mourning something which is clearly within our power to rebuild when we can get within a few feet of where it used to be? Even in sheer number of mitzvot which could be done with a temple than without. Is it not better to make those mitzvot accessible than keep them locked away under supposed promise of a magical building descending from the sky and probably setting off WW3 in the process?
Tzom Kal, and may this be the last Tisha B’Av fast.