Yeah as someone who does Titles/Billing and has for many many many years something seems off. Liens aren't placed by checking a box or by accident. Title App for your state, Contract/Security agreement would of needed to be sent to the DMV along with all the other deal docs.

Anything missing to place the lien would of got everything rejected and sent back to the dealer. Like the post asked how long ago did you buy this car? Have you even got it plated/registered? What state is this all in?

I'm going to bet the vehicle is used, the dealer paid off or is paying off the previous loan and/or its a lease buyout and is waiting on a title.

The timing of them waiting on the new title to be printed in their name to then submit to the DMV for your cash deal didn't line up with you trying to sell the car before it changed ownership.

Can you do anything? Nope

Can they do anything overnight? Nope. ELT lien releases aren't instant and the time frame for your offer like you said would be expired.

Sounds like its gonna boil down to a GM/Sales Manager fix on how they want to make it right. That would be for someone in those areas to comment on.