There are two things related to financing.
First, is the order task that requires you to select Cash, Leasing, or Finance. If you do not complete that task, evidence suggests your order is not placed into queue and you will never be assigned a VIN.
Second, is the payment itself, necessary before you pick up your car, but NOT before a VIN is issued.
Since Tesla financing, once approved, is only good for 60 days - and assignment of VIN and scheduled delivery may take longer than that - the best thing for many is to simply select 'Cash' when ordering their vehicle (thus completing that 'finance' requirement); and then change 'Cash' to 'Finance' once a VIN is assigned.