Have you contacted Tesla? I reached out to them to add financing to my order after I got my VIN last night and the guy I dealt with (who was regional sales support or some such title) was extremely helpful. He told me which day the car was showing that it was due at my local delivery center (19 Jan), that it usually takes 2-3 days from then until they're ready to deliver, and that I should be contacted in the next couple days to schedule it. He also spoke with my delivery center and put me in for home delivery at my request, and cleared up several other questions I had.
I'd try contacting them if you'd like more info, but from what he said it's usually at least 2-4 days from receipt of VIN to scheduling, but I suppose that could be different depending on your timeline.