I Started a business and as part of that leased a vehicle. I paid a down payment. Can the down payment be listed as part of the start up costs?

No, you can not claim the down payment as a deduction on your taxes.  It is not deducted in the year of payment. However, it can be amortized (deducted) over the term of the lease. 

• If the vehicle is used exclusively for business, all of the expenses (within limits) can be deducted.
• If the vehicle is used for both personal and business use, the portion used for business may be deducted.
• There are to options for the dual use scenario:

You can choose between two methods of accounting for the business mileage deduction amount: 

• The standard mileage deduction 
  • For 2023 is 65.5 cents per mile for business
  • IRS Mileage rates
  • If using standard mileage, it must be chosen in the first year the vehicle is in service
• The Actual Expense Method requires the mileage log plus details of all expenses.  This includes fuel, repairs, oil changes, tires, depreciation etc.

Please se the TurboTax article Business Use of Vehicles