There MUST be a temple for the AOD to occur in. The AOD was first prophesied by Gabriel to Daniel, then by JESUS to His disciples. It's quite clear that event is gonna occur!
It simply did not occur in the old temple.
Jesus said -
Mat 24:15 “Therefore when you see the ‘abomination of desolation, spoken of by Daniel the prophet, standing in the holy place” (whoever reads, let him understand), 16 “then let those who are in Judea flee to the mountains.
Luke 21:20 “But when you see Jerusalem surrounded by armies, then know that its desolation is near. 21 “Then let those who are in Judea flee to the mountains, let those who are in the midst of her depart, and let not those who are in the country enter her.
22 “For these are the days of vengeance, that all things which are written may be fulfilled.
Luke 21:20 “But when you see Jerusalem surrounded by armies, then know that its desolation is near. 21 “Then let those who are in Judea flee to the mountains, let those who are in the midst of her depart, and let not those who are in the country enter her.
22 “For these are the days of vengeance, that all things which are written may be fulfilled.
It happened, so the believers left the city & area & fled to the mountains.
A temple built by professed Jews who reject the Messiah will NOT be "THE holy place."