God let the Mohamedins occupy the Temple Mount only to keep it out of the hands of Christians until Jews were ready to repossess it.
Last time I checked, relatively few Jews care to rebuild a Temple and be burdened with the constant beat-down of slaughtering critters, while its the Western Premillennial Dysfunctionalists "Christians" who are raising money, breeding red hefers, weaving temple garments, fashioning temple furniture and shouting down orthodox Christians while conjuring up ways to trick the Muslims into abandoning the site.
If the cult of Hal Lindsey had control of that scratch of land, the Temple would soon be listed among the Seven Great Wonders of the Modern World.
The End Times Christian fantasy of millions of dead Jews with the rebuilt Temple bears no relationship to its actual eventuality.
You’re right: End Times fantasists have no idea how difficult rebuilding the Temple is, frequently mistaking tourist attractions for the real thing.
If Agudath Israel of America and Chabad aren’t endorsing any attempt, it ain’t happenin’ any time soon!