No, what we can assume is that we don't know. In any case, to be correct about things we already knew is not so hard. It's being right about things we didn't already know that would have made some impact.
Which is why I'm confused that you blew off so many things that were not known when the BoM was written: dozens of new proper names from the Amarna letters and Elephantine Papyri, both of which were discovered afterward; the Kurtz data on Hebrew speeches, discovered only a few decades ago. The Works of Ixtlitlxochitl languished in a dusty library for centuries before being translated into English. Are we to believe that Joseph had a Spanish-speaking accomplice who snuck over to Europe just to rummage though old books!?
There's plenty more:
* quellenlieder speeches were not known at the time of Joseph Smith, but a textbook case of one appears in the Book of Mormon. How do you explain this?
* no one had ever heard of writing on metal plates before, but we have dozens of examples now. How did Joseph know this type of writing existed?
* the ancient Iranian banner-epic was discovered after the Book of Mormon, yet Captain Moroni's Title of Liberty is a perfect proof text. How did Joseph Smith come up with this?
* the account of the remnant of Joseph's coat was discovered after publication, yet it is cited by Captain Moroni when he creates the Title of Liberty. How is this possible?
You've got to deal with things like these if you really want to claim that the Book of Mormon is a fraud, or that Joseph fabricated it. "Fraud" is an act; you must show participation in the act. If someone is on trial for murder, it's not enough for the prosecutor to demolish his alibi, if the defendant cannot be tied to the crime, he goes free.
Likewise, showing a lack of evidence in the Americas is not enough to cry fraud. You must explain how Joseph got any of these things right.
Before, you claimed these were coincidences. Consider that the Kurtz data alone would be validated only 1 in 20 factorial times (20*19*18*17...*5*4*3*2*). Adding the astronomical chance of matching a dozen or so dates from the Works of Ixtlilxochitl...and all six points of a quellenlider...and one wonders if the lack of data might be an easier coincidence.
I don't believe that the above is sufficent archaeological proof that the Book of Mormon is true.
But saying it's a "fraud" is a positive statement. Burden of proof is on you to prove it's a fraud. And that means you need more than a coincidence cop-out. After all, if we're willing to entertain trillion-to-one coincidences, why not just allow the coincidence that all thes things really happened, but all the evidence happened to disappear?
(I know this was a long post, but I can offer source texts for any of the above. You need only ask!)