I'd just start the application now and get a conditional approval first based on how much you're wanting to borrow. You can get an estimate of the cost of the vehicle through tesla's check out page. You're allowed to borrow up to 125% of the vehicle's value so if you wanna include your tax/registration cost added in, you can as long as you meet their credit score, credit history, and debt to income ratio.
Once you have the loan conditionally approved, then you can put in the order and send whatever documents that the credit union needs (probably invoice, vin, etc.). Once you do that, they'll set up the payment with the Tesla SC.