Has construction of the Tribulation Temple begun yet?
No, construction of the Tribulation Temple has not begun yet. The context states it is still future from our present time, though the Jews are more than ready to rebuild their next temple. It will be built, but Scripture indicates this rebuilding occurs before the middle of the Tribulation.
Les explains that the Tribulation Temple will become the third temple, after Solomon's temple and Herod's expanded complex. He notes that if you watch current events, the Jews are more than ready to rebuild their next temple, yet from our point in time today it is still future. Les teaches that it has not begun to be built as yet, but it will be. This is one of the proofs from Scripture that a temple will be rebuilt in Jerusalem at some point before the middle of the Tribulation. That, he says, is all we know.