New Loan Opened in Quicken Shows as Paid Off,

You've clearly established this loan as a "downloading" loan. Search this forum and you'll find this complaint comes up frequently. This information is typically downloaded using one or the other of the Express Web Connect downloading method and for whatever reason this method is not terribly reliable, not infrequently resulting in what you're seeing. Downloading loans also have no loan register that you can affect as the fiction is that the loan company is always going to send you "perfect" information, but that's not always the case. (This goes back to the unreliability of EWC, not that the loan companies don't know what they are doing.)

Personally I see absolutely no point in making a loan a downloading loan; the only information that's downloaded is principal payments, not interest, not escrow, and all that information is available to you over in the checking Account you're using to make monthly payments. You can reverse your decision to go with a downloading loan by simply deactivating the Account from downloading. That should give you access to the loan register. "Good housekeeping" here does dictate that you periodically check to see that the balance of the loan Account agrees to the lender's statement.