there is much discussion on here about the subject, even some tracking statistics. FWIW, my Model 3 LR shipped from Fremont to central Florida on Sep 4, and per schedule I took delivery on the 21st, my DD. That was about 2.5 weeks shipping cross country. My OD was in May, about 4 months OD to DD.
Like you, I and others got little status/progress info, and when or how often we got it was not very predictable. The emphasis on text messaging added frustration for me.
At some point they'll inform you a VIN has been assigned, then you'll get notification of shipment, then a message asking you to schedule delivery, picking from a few dates they offer. I don't know when mine arrived at the service center (they offered t but at location only), but I suspect it was less than 48 hours before delivery.
Working out final agreements and payment and financing it often confusing too, aggravated by uncertainty about when each upcoming milestone is to be set. My credit union uses different terminology than Tesla for financing. Tesla's use of texting to finalize things is not what lenders are used to.
Good luck, with the process and with remaining patient/calm ;-)