If I understand correctly, the third temple that is to be built seems so pivotal in the last days and 7 year tribulation. Is it the anti-Christ that gives the order or approval after the signing of the peace treaty to begin building the third temple? How long could it take to build this third temple with expected work crews that could be available? If it takes 20 years to build the third temple, does that move the possibility of the Rapture further ahead as well?
The building of a Temple in Israel and the rapture of the Church are not related. The rapture can happen any time now, but the Temple will be rebuilt only after Israel has returned to its Old covenant relationship with God. I believe the anti-Christ will help clear the way for the Temple to be rebuilt, but Daniel 9:27 says he will also cause it to become desolate 3 1/2 years later, putting an end to sacrifice and offering. This means the Temple will have been in use for some period of time before he does this.
I don’t know of any credible estimates on the time it will take to build the Temple. Some think a temporary structure could go up very quickly. Others say the materials have been secretly gathered and only need to be assembled. It seems to me that as soon as the rapture takes place other things will start happening very quickly. But what ever the case, I don’t think the Church will be here to see it happen.