She said that "this is a mystery that has been going on for hundreds of thousands of years" (00.28 seconds into the video).
The Ark was reportedly constructed by the Israelites soon after they began the Exodus, which can be dated to roughly the 13th Century BC. So even if the thing exists still, it's only a little more than three thousand years old, not a relic of the Paleolithic period.
I'm certain the Ethiopian Orthodox Church believes the thing in their Cathedral is the real Ark. But Jeremiah 3:16 seems to imply knowledge that it was destroyed: "it shall not be made again." Probably people were aware that the Babylonians destroyed it along with the first temple.
But it was fun to see a segment on ancient relics and Orthodoxy. I'll celebrate by opening a bottle of Ethiopian Orthodox beer that a friend brought me, also not Paleo.
To the praise of St. George. To the faithful of the Ethiopian Orthodox Church. To your health, Nadia Bilchik. Many Years!