Is there any historical evidence that the Ark of the Covenant really existed? What physical or written evidence is there, excluding the scriptures?
Note: I am not discounting the writings of the Bible or Christianity. I am asking if there is any other writings without the pretense of Christian association that mentions the Ark or any other physical evidence.
Outside of the Bible (both the Hebrew Bible and the Christian Bible) and related literature (such as commentaries, but not excluding historical accounts outside the Bible) there are some references.
Flavius Josephus makes numerous mention of it in Antiquities of the Jews (For examples, see Book 3 Chapter 6 Part 5, Book 5 Chapter 11, and Book 8 Chapter 4) and one mention is Wars of the Jews (see Book 5 Chapter 9 Part 4). In Antiquities of the Jews, he tells of a tradition that "sacred vessels" have been hidden in Mt Gerizzim by the Samaritans (see Book 18 Chapter 4 Part 1). Some believe one of the "sacred vessels" may include the Ark of the Covenant, but this most likely is inaccurate.
In Ethiopia there is a place where the Ark of the Covenant is claimed to be held. They have a person who spends their whole life guarding the place. He is the only one who is allowed to see the Ark.1 If an "Ark" wasn't there, I doubt he would still be guarding it.
In the second book of Maccabees, we are told the prophet Jeremiah hid the Ark prior to the destruction of Jerusalem.2 (The Books of Maccabees may or may not be considered biblical.)
More information concerning it can be found on Wikipedia.
Addendum:
Since "Nope" is probably not a very good answer, let me explain.
There are numerous references to the ark of the covenant throughout the biblical literature. Its construction is described in laborious detail twice in the book of Exodus, it serves as the receptacle for the words of "this song" (understood by subsequent exegetes as the Pentateuch, or at least the book of Deuteronomy) at the end of Deuteronomy, it gets taken captive, redeemed, is venerated and placed in the new temple in Judges, Samuel and Kings, and then is presumably removed from the temple by the invading Babylonians... who never mention it in any of their archival records.
This literature is the only literature that mentions the ark. But note that there is not a single part of this literature that was authored with the intention that it be a part of a "bible", which means that the books of the bible can all be viewed as independent of one another. Not only that, but they are themselves a pastiche of multiple sources, which means that there are dozens of different texts right here that all testify to the existence of this thing (or to traditions concerning its one-time existence).
References to the ark in works like those of Josephus don't count, since he's getting all of his information from the biblical literature. In fact, references to the ark in any post-biblical literature don't count for that very reason, while references in extra-biblical literature contemporaneous with the Bible's composition don't exist.
Later religious traditions have come up with explanations as to what happened to it: that it was hidden away beneath the floor of the second temple, that it was spirited off to a far away land (read: Ethiopia), or that it was secreted somewhere in the foothills of Judea. These traditions are all bogus. There is no ark. And since it was made of gold, we can assume that if there ever had actually been an ark, it has long since been melted down and turned into something of more practical use.
All proof is non-religious, more or less by definition. Faith does not require proof.
As for the empirical evidence of the Ark's existence, no, nothing's been found to satisfy a sufficient number of historians, archeologists, theologists, etc. to be declared official.
