It is possible to deduct a new car purchase per IRS regulation. However, if you deduct the expense of a new car (such as car payments and depreciation), you wouldn’t be able to deduct your mileage!
The standard mileage rate is calculated to be inclusive of the car payment and depreciation costs that you would deduct. You can only use the standard mileage deduction if you don't use the "actual expense method," which involves deducting a portion of all of your vehicle costs—like gas, maintenance, car payments, etc. Depending on how long you intend to be using the car for work, it may be more effective in the long run to take the standard mileage deduction.
Here's an article that explains the difference between these two methods: How should I deduct my vehicle expenses?
I would recommend looking at your estimated mileage deduction for this year against your costs for the new car, and deciding if deducting your car payments would give you a higher deduction than your mileage.
Note: If you use the actual expense method this year, you're required to use that method for the rest of your car's life! You won't be able to switch to the mileage deduction in later years if you're using the same car.