Further update - got the HR Director at my employing company to write up a letter saying that I have started employment with the company and am currently staying at the company's corporate apartment at <address>. The bank accepted that, so checking account opened and debit card already in my wallet.

Hmm.. that's a concern. The validation letter basically says

"This is to acknowledge that you applied for a Social Security number on October 3, 2016.

Before we can issue you a Social Security number card, we must verify the document(s) you gave us to show your Alien status with the Federal, State, or local office in the United States that issues the document(s). The may take up to 4 weeks."

Not sure if that means it's been put into manual verification or not - if so, I guess there's not a whole lot I can do about it now.

Sounds like it to me. If you were already in their system, you wouldn't have received such a letter.

We usually recommended waiting a week or two before visiting the SS office, to make sure you are in the system.

Rene

Yes, it looks like you've applied too soon unfortunately

Ah well, that's rather unfortunate, but it is what it is. Thanks again folks.

For what its worth, the DPS (Equivalent DMV in Texas) accepted the SSN letter saying that the application had been submitted, with my US address on it as proof of address, as I was in the same situation as yourself in regards to the lack of proof. Any letters from a state or federal institution were accepted. Outside of that I had a bank statement which you may also be able to provide now

Good luck, also make sure you have EVERYTHING with you (including printed i-94) when you get to the DMV and if possible have additional proof of address. I took a letter from my bank originally as I had literally opened the account the same day and they refused it saying it HAD to be a statement (a load of tosh, considering the documentation merely said a letter from a financial institution, but hey ho)

relocation advisor's tip...
you do need a bank statement for DMV but just go into any branch and ask them to print one out for you. Even if you only opened the account an hour beforehand you can get a statement this way.

This is also a good tip for younger drivers (ie your kids) who may not have utility bills etc for proof of address.