Orthodox Israel denies Jesus is Messiah. They believe messiah is yet to come. Therefore they aspire to build a temple.
even if they were to build one ... the Shekhinah glory (presence of God) will not enter it.
Matthew 23:38 (Jesus speaking) “Behold,
your house is
left unto you
desolate.” Jesus prophesied the city and the temple's destruction. To His own disciples, He said just three verses later, “There shall not be
left here one stone upon another, that shall not be thrown down” (Matthew 24:2).
Luke 19
Berean Study Bible
They will level you to the ground—you and the children within your walls. They will not leave one stone on another,
because you did not recognize the time of your visitation from God.”
Jesus never entered the earthly temple after that. He is our High priest and ministers from the heavenly sanctuary ... the REAL one ... not one made with hands.
The earthly temple (even if were rebuilt) would remain desolate until Jesus returns.
Personally I don't believe it will be built ... but if so it will all be in vain.
We have an inner temple that shares spiritually with the heavenly temple until He returns ... THEN we will enter the heavenly temple both spiritually and physically. Amen!