I suspect that the advice you have had on the Toyota forum is correct and the dealer is waiting for order slots to become available to them. This is a problem that crops up continuously with lots of dealerships, not just Toyota. People understandably don’t appreciate that when they think they are placing an ‘order’, all they are really doing is expressing an interest. The actual order is placed at a later stage between the dealer and the manufacturer. If the dealer has available build slots, the order is usually placed within 24 hours or so. It’s not a chassis number you are after by the way, it’s an order tracking number. VIN numbers aren’t allocated until the car is actually built.
When considering ordering a new car I always ask the dealer if they have any immediately available build slots for that particular car. If they don’t I try another dealership. Problem is that many lie and imply that they have order slots when they don’t, just to get the business. Countless people on this forum have experienced this and don’t realise until they have waited a month or more and not heard anything.
In your situation I would ask the dealer to tell you honestly if they are waiting for order slots to become available. If the answer is yes, ask another dealership and consider moving to them if they have immediately available order slots.