No, the financing options include the Apple Card Monthly Installments (ACMI) and the iPhone Upgrade Program. neither of which have an option for a "down" payment.
For the ACMI you can make pay the installment, and then make an early payment to reduce the balance in that amount.
How to view and pay Apple Card Monthly Installments - Apple Support
To pay extra on your Apple Card Monthly Installments, you need to first pay your entire Apple Card balance. Then, to make an additional payment towards your installment balance, choose Pay Early. If you have multiple installments, your extra payment is applied to the outstanding balance of your oldest installment plan.
A similar thing can be done with the iPhone Upgrade Program, though you must be in the program at least 6 months before you can upgrade.
If you choose a carrier financing option, you would need to inquire with them if you can pay an amount upfront and then finance the rest or not.