My experience -
I paid cash i.e., no financing. I mode of payment I chose was cashier's check because I didn't want to use Tesla's Plaid service. This caused some unnecessary delay. After I sorted it out with one of the Tesla advisor (don't know if they're called SAs), I was advised to email her a copy of the cashiers check. After which the delivery got expedited.
When we went for the pickup, the car was in the slot that was mentioned in the SMS message. We could see the car from outside but to access from inside we had to go see the service desk where we're asked to pay the cashier's check after which we had to accept the delivery in the app before getting access to the inside of the vehicle.
So my take is that there is no point in holding up the payment. One can always refuse to accept if there is a major issue with the vehicle. But that's my opinion.