Archeological Proofs - The Existence of the First and Second Temples
The background of The ARK Report The Quest of All Time includes extensive historical research.
One of the primary archeological discoveries that support the theory of where the Ark currently sits can be found in the book
In the Shadow of the Temple: The discovery of Ancient Jerusalem
by Meir Ben-Dov (1982). In the book, Ben-Dov tells of his discovery of the secret tunnels carved out of the rock underneath the Temple Mount's gates. These tunnels enabled the ritually impure Kohanim to leave the consecrated area of the Temple and descend into the small cistern that served as the ritual bath. As the entrance to the tunnels was deliberately blocked, they cannot be followed to the end. It is at the end of these tunnels where, according to all opinions, we would find the exact location of the chamber and subsequently the rest of the Temple complex.
There is a confirmed channel (tunnel) to the underground chamber where the Ark is being kept which extends from a secondary, southwesterly passageway that may be reached by means of Warren's gate. During an investigation held immediately following the Six-Day War, Rabbi Meir Yehudah Getz, then Chief Rabbi of the Western Wall, and Rabbi Shlomo Goren, then Chief Rabbi of the Holy Places in Israel discovered a vaulted chamber, thought to be the original entrance to the Temple Mount from Warren's gate. From this, another, lower chamber was also discovered. According to the testimony of the two Rabbis this chamber also had a passage directly into a room filled with vessels possibly dating from the time of the Tabernacle. This was never further pursued due to fears of creating another major regional war.