[ducttape45]

That platform was a Roman camp. The Temple of Solomon stood to the south, and down from, that encampment.

Act 21:30-32, "And all the city was moved, and the people ran together: and they took Paul, and drew him out of the temple: and forthwith the doors were shut. And as they went about to kill him, tidings came unto the chief captain of the band, that all Jerusalem was in an uproar. Who immediately took soldiers and centurions, and ran down unto them.

The soldiers ran down from the Roman encampment that the Jews call the Temple Mount.

[Cronos]

Actually it wasn't the Roman camp - it's too large for even a legion. Also, the Roman camps had timber walls, not stone.

The western wall is a relic of the base of the temple mount.

Josephus, the Jewish historian who lived in the generation after Herod, records that the Antonia Fortress was *North* of (an already existing) Temple (see his Wars 5:5). I believe that he also indicates that the Antonia was built *before* Herod extended the Temple Mount platform, which necessitated a landfill buttressed/ supported by a wall along its western side. A small portion (roughly 1/7th of the total length) of that new, supporting wall is what is today exposed and referred to as the Western Wall (Kotel).

At best, one might argue that this supporting wall’s northernmost end (hidden away today behind buildings in Jerusalem’s Moslem Quarter) was an extension of the Antonia’s own western wall.

here's a model of the Antonia fortress

you are repeating Robert Cornuke's statement but it doesn't reconcile with what Josephus wrote nor with the archaeology on the site