My timeline in case this may help anybody going through this glorious process at the moment. I found the 'wait' to be the easy part (this thread helps a lot), and then the crazy rush in a small timeframe to be the stressful part.
-OD 8/20.
-Zero contact with Tesla.
-Vin Arrival 10/26, accompanied by an email saying "final payment is due".
-At this point my EDD was November 8-18.
-Sometime during the next week it moved to November 7-13. Which was a bit terrifying because I was still selected as "cash" in the system, needed to switch to 3rd party financing and begin work on my Trade.
-Somewhere towards the end of this week my EDD moved again to November 3-9.
-Used the chat feature to change my financing and tie the trade estimate I had to my account on the 26th.
-The system took until Oct 31 to update my trade-in information, which included an email from the "PayoffQuotes" team to get the information for the current loan on my trade.
-I spent a few days of the following week lining up my financing, which was not exactly easy as I was on work travel, and Tesla doesn't provide things like a window sticker that my lender was looking for. The MVPA was also not updated until -11/3 to show 3rd party financing and a spot for both Tesla and myself to sign the agreement.
-Got emails and phone calls from Mt. Kisco on Thursday 11/4, which culminated in them asking if I wanted to take delivery on the 5th. I have another post going through the confusion for that day.
The part I thought most interesting is that I had no contact from anybody directly at Mt. Kisco, not until I was 4 days before my original delivery date of the 8th that they tried to move up. If my car did not come in early I bet I would not have been contacted until 2-3 days before delivery. When I called their number on the 5th ensuring I was scheduled for pickup that day, the person said, "I'll send your delivery team a message and call you back when they answer". I said, "No, I'd like you to walk over there and ask so that I know I can leave my house". He then informed me that he is not physically located at Mt. Kisco and it was a call center. When I arrived I saw why, the showroom is tiny, and it was full of a bunch of people looking for test drives, supercharging, and asking questions/ordering.
TL;DR - I wouldn't expect contact from your specific delivery center until they have your actual car in their posession, that gives them the fire they need to ensure they book the sale quickly.