Sorry I don’t know whom you are quoting, but IMO that answer is wrong.
The looting of the Temple by Nebuchadnezzar is described in 2 Kings:
"24:11 And Nebuchadnezzar king of Babylon came against the city, and his servants did besiege it.
24:12 And Jehoiachin the king of Judah went out to the king of Babylon, he, and his mother, and his servants, and his princes, and his officers: and the king of Babylon took him in the eighth year of his reign.
24:13 And he carried out thence all the treasures of the house of the LORD, and the treasures of the king’s house, and cut in pieces all the vessels of gold which Solomon king of Israel had made in the temple of the LORD, as the LORD had said."
So either the Ark was not in the Temple then, or the authors of 2 Kings did not think it was important enough to merit special mention. This would be approximately like a police report of a burglary of the US National Archives saying that various documents were stolen, and not bothering to mention that the original Declaration of Independence and Constitution were among them.
According to the book of Ezra, after conquering Babylon about 60 years after the event described above, Cyrus allowed the Jews to return to Jerusalem and rebuild the Temple.
"6:5 And also let the golden and silver vessels of the house of God, which Nebuchadnezzar took forth out of the temple which is at Jerusalem, and brought unto Babylon, be restored, and brought again unto the temple which is at Jerusalem, every one to his place, and place them in the house of God."
So that verse indicates that at least some of the treasures of the Temple were not cut up or melted down, but were preserved intact. As the most holy object of the Jews, the Ark would likely have been one of them. And again, there is no mention of the Ark, not even a lament over its loss.
The obvious conclusion is that the Ark was not in the Temple when it was sacked by Nebuchadnezzar, and nobody knows when or why it disappeared. As it was allegedly kept in the Holy of Holies, where nobody was allowed to see it but the King or the chief priests, it could have been gone for decades before the destruction of the Temple, with only a few people knowing it was missing.
Or more likely, it never existed.