Did you sign the stack of DMV papers that came with the car and submit it back to your delivery center for them to send into the DMV? The registration being discussed here is not the temporary registration, it's your car's permanent registration. That stack of papers has sometimes been said to be lost in the process and owner had to go back to store or delivery center to fill out new copies. Sometimes it is the delivery agent that didn't make it clear that the paperwork needed to be submitted back to Tesla, and the owner just never did so.
As for processing time, it has been said that Tesla may submit to DMV in batches so it may not be immediate.
Here's the timeline for mine (I had contact-free delivery and sent in the paperwork that was inside car in the given FedEx envelope):
12/31/2020 delivery, Colma Delivery center received my paperwork 1/4/2021 via FedEx, title date 1/15 (post mark 1/28), got title 2/1, got plates and registration 2/11