Do we have a biblical command to rebuild the temple once it was destroyed? And where does a command exist to build a temple in the first place?
The command to build (and re-build) the temple appears in Torah. Where?
Actually about 1/3 of the whole Torah is dedicated to it building (and re-building).
“…make a sanctuary for me, and I will dwell among them.” (Exodus 25:8)
“Then I will dwell among the Israelites and be their God. They will know that I am the Lord their God, who brought them out of Egypt so that I might dwell among them.” (Exodus 29:45-46)
Remember the Temple (Beit ha'Mikdash) became another term for the Tabernacle (Mishkan).
But both refer to the same place.. Mikdash meaning a place a holy place from qud's (ie Al Quds) and Mishkan meaning a place of dwelling. (ie Shechinah).
And remember the tabernacle not only was build and torn down many times, it was even mobile.
However if there is no Ark (Aron ha'brit) there is no tabernacle/temple and if their is no red heffer (parah adumah) their is no tabernacle/temple.
Which places the whole 2nd temple in a dubious position. (Because there was no ark).
So because we lack these two crucial items including other less important items like Urum v'Thumim (Holy dice), the temple is not expected to be re-built anytime soon at least by earthly means.
*(there are also rabbinic opinions that teach that the (potential) Messiah is a pre-requisite to begin its construction.) ~Hil Melachim Chap. 5 Halacha 1
R' Asher Meza