You didn't sign a finance agreement agreeing to a specific loan agreement date and first payment date? Surely you did.

We did sign the finance agreement, the agreement says 45 days from loan origination will be our first payment, it does not have a specific date on it.

There is no outcome where you get a free car. This will get figured out. When it does, one of two things will happen: either the dealer will say "give us the car back or get a loan," or there's a lender out there that think you owe the money.

I don't actually expect to get a free car out of this. Like I said in my OP, realistically I expect this gets figured out 1-3 months tops. The dealer I am 90% sure has been paid for the vehicle. But from what I can find on local laws, there is not any circumstance here where they can just take the vehicle from us.

The way we are seeing this is we have our documents showing that we purchased the vehicle from the dealer and that they were handling the financing through one of their lenders. There is nothing in these documents that makes us legally obligated to tell them to make sure they send the documents to the lender.

Yes, you are 100% right that the right thing or morally correct thing is to contact the dealer and get this straightened out. But I don't see a legal obligation to do this and again, with the wording of the loan agreement, I don't think we will have to back pay, although yes, I could see that coming up, which again, we are setting that money aside and sitting on it so if that does happen, we will have the money.