Answer
When the Bible lists the many things that the king of Babylon took with him before destroying the Temple of Jerusalem, the Ark of the Covenant is not mentioned. The Jews who rebuilt the Temple only seventy years later did not find the Ark, and it seems that at that point it did not exist anymore. It is likely that the Ark of the Covenant had already been destroyed. From a Babylonian perspective, it was a piece of wood overlaid with gold, and so the Babylonians would have simply wanted to strip the gold and burn the wood. Therefore, the best answer to your question would be that the Ark of the Covenant most likely did not survive the Babylonian destruction of Jerusalem and the Temple.
The Second Temple that existed for six centuries (515 B.C.–A.D. 70) functioned without the Ark of the Covenant. According to Jeremiah 3:16, there will also be no Ark in the Millennial Temple. The point is that the Ark of the Covenant was not essential for the atonement to occur since the key element of the atonement was the shedding of blood (Leviticus 17:11).
