The Waqf, Jordan, the Palestinian Authority all claim there's no archaeological scientific proof of the existence of a Jewish Temple on the Temple Mount.
Well, read this from a review of a study edited by Gideon Avni and Guy Stiebel, Roman Jerusalem: A New Old City, in the Journal of Roman archaeology. Supplementary series, 105. Portsmouth, RI: Journal of Roman Archaeology, 2015:
The second part of the volume (The ritual sphere) has two fascinating contributions...the other by Perez Reuven about a decorated beam removed from the al-Aqsa Mosque during renovations in the 1930s. The beam of cypress wood is 12.5 meters long and based on its decoration is dated by Reuven to the second or third century; it originally was part of an architrave of a monumental building in Roman Jerusalem. Reuven hypothesizes that it may have been part of a temple on the Temple Mount, which brings us to the debate about the presence of a temple to Jupiter on the site of the destroyed Jewish Temple and the fate of the Temple Mount."
It has been theorized that the beam was in secondary use:
High-quality Cedar of Lebanon and cypress beams from Herod’s Temple Mount would have been used and reused in a phenomenon known to archaeologists as “secondary use.” R.W. Hamilton’s 1949 publication on the dismantling of the Al-Aqsa Mosque already noted that many beams showed signs of secondary use. These signs include functional depressions or protrusions intended from their original use as well as decorative woodcarving styles from earlier periods.
Recent carbon-14 tests on the beams confirm their antiquity. Some predate Herod’s Temple Mount: One beam dates to the ninth century B.C.E.—the First Temple period! The exact history of the beams is hard to pin down. They were likely used in two or more different constructions, and poor storage has led to the ever-quickening degradation of the beams.
Despite conservation issues, Peretz Reuven was able to make detailed analyses of the beams. For example, indentations on the underside of a beam with Herodian/Roman-period decorations suggest that it rested on column capitals in an earlier structure. The indentations are spaced at a similar interval to columns at Herod’s Royal Stoa.
The beams were for years stored outside, next the the southern wall, suffering from the elements:
and now for the past few years in the courtyard of the Double (Golden) Gate:
I presume they are rotting away.
UPDATE
And as it happens, the next day, Friday, after I posted this, Arnon Segal wrote on the same subject in his weekly Makor Rishon page dedicated to the Temple Mount and included this picture of various beams from different periods. The earliest Roman beam is on top:
^