In Feb of 2020 I saw my first car sit on a Portable Parking Lot for about 8 hours. Then it disappeared inside the Service Center. Then it was 4 days before I was able to pick it up. I was told it had to be put in line for inspection, final prep (!), then it was detailed (and I have to hand it to them, it was spotless and shiny), then there was some administrative delay over getting the state inspection and paper plate.
IIRC in NJ, there are no paper plates, you hve to have the Official plates before you can get your hands on the car. So I guess a week is typical to wait for all the functionaries to do their thing. I think it is cruel for them to tell you the 27th, though. There's a country song called "Tell Me A Lie"...