Already answered. Hagai was chronologically between the building of the First Temple, its destruction, and the building of the Second. Both were built by human effort. It is not determinative, however, of how the Third Temple will be built.
In a very real sense, we are building it right now, with the Mitzvot that we do, each of which brings the final Redemption of the entire world and the rebuilding of the Temple that much closer.
Personally, I would be in favor of making bricks right now, for the construction of the gates, which is incumbent on us to do, and on each brick to engrave the name of someone who was murdered ‘al kidush Hashem’ (to sanctify G-d’s name), starting with the most recent victims of terror, and going back as far as there are names of the victims. I do not, however, know how to kiln bricks, or how to engrave names on them, let alone possess a kiln and a stylus, and don’t have enough time to compile all the names.
But all this is does not involve destroying the Muslims’ golden potty, deliberately looking for all-out war, or anything quite so drastic. For all we know, the war of Gog and Magog might become subliminalized into a spiritual contest. If it becomes a great and terrible physical confrontation, it will do so on its own, though. No need to deliberately light the fuse. In the end, the Third Temple will be there, and the mosque will not. Our role in bringing that about is not specifically detailed.
Harsh prophecies can be sweetened by our good actions. Prophecies that bestow good on someone are never corroded. Thus, because G-d promised to make Moses into a great nation, there is a great nation descended from Moses somewhere (this from the Talmud, Berachot, I forget what page, but in Chapter 1). But G-d also said in the same breath that he would destroy the Children of Israel. That was not fulfilled then, although in every punishment inflicted on us, a small portion of the sin of the Golden Calf is also repaid.
Fair enough, how do we know then how the Third Temple will be built? Or more to the point, are you saying that those people who have a cornerstone (and quite a few other stones) ready are wrong in doing so? I know the fellow who started the Temple Mount Faithful is convinced that the Lord wants the Temple rebuilt in this generation.
with the Mitzvot that we do, each of which brings the final Redemption of the entire world and the rebuilding of the Temple that much closer
Wouldn't that be nice? Yes, I would like to think that there's something I can do to bring about the Messianic Age any sooner.
does not involve destroying the Muslims’ golden potty, deliberately looking for all-out war
It's been a while that I read the Northern wall of the Temple Mount is bulging, could collapse with a small tremor. So, maybe there will be no need to deliberately destroy anything, although such a collapse will be blamed on Israel and war just as likely as if y'all dropped a MOAB on the mosque.
this from the Talmud, Berachot, I forget what page, but in Chapter 1
Is it available on-line, in English? More important, would I be able to understand any of it?