There is nothing in the Bible that says the temple needs to be built EXACTLY on the temple mount, exactly where the Mosque is now. In the spring of 2003, Orthodox Rabbinical students argued that point by laying a figurative corner stone at the border of the disputed area next to the wailing wall. It caused all sorts of ruckuss at the time but it supported an opinion I’ve had for a long time that there is nothing literally stopping the temple from being built except for God’s timing. The Bible says the temple will be rebuilt, it doesn’t say it will be rebuilt exactly in the same place as the other two were! It is conceivable that both mosque and temple could exist side by side for a time!
Prophesy states the Temple will be built where that mosque is now. If it’s not, then it’s not the rebuilding of Solomon’s Temple. It’s some other structure. Heck, they could build it now and then call it the “Temple” and we’d be done with it. Maybe.
Read the Book of Daniel