When you signed the papers, all that is promised is that they will try and find you one like you requested by making a request to the distributor, Hyundai Motor America (HMA). Other dealers want the same cars, so they have to wait until HMA allocates it to that dealer and delivers it to their dealership. The dealer does not own the car until HMA delivers it to them. In normal cases, dealers might trade cars with other dealers, but not very likely these days because everyone is in short supply.
In "some" cases, dealers are giving cars to newer customers (those who "ordered" one after you) if they are paying more than you are, and there is nothing can do about it other than cancel the deal and try another dealer. The "paperwork" you signed keeps you from shopping at other dealers who might be able to get the same car faster, unless you cancel the deal (not sure what the cancellation terms are). So when they say they are expecting the car in on a certain date, they may be telling you the truth or may be stringing you along so you don't go somewhere else or buy a different brand. But in general, Palisades have been in short supply for awhile, just like a lot of other products. The shipping ports in the LA area are some of the most congested in the world right now and the Palisade is made in Korea.