As described by you, there is no way to avoid probate. Probate avoidance must be done by a person before he/she dies.
The only possible way you can avoid probate for the vehicle is if Dad had a TOD on the Title to the vehicle. If not, and if the vehicle's current value is less no more than 5,000$ (but less than the amount paid for the funeral) then the person who is named on the "paid" funeral bill can file forms at Probate Court to obtain a court order directing transfer of the title to that person.
This process might not be available if the total gross value of all probate assets is in excess of the 5,000$ limit.
You will need to look at the certificate of title to see whether your father named you as a transfer on death beneficiary of the car. If not, the car will need to be probated, together with any other probate assets he owned at the time of his death. If the car is the only probate asset it is likely that you will be able to have the estate relieved from full administration, which will minimize the expense of probate.
This reply does not constitute an attorney-client relationship. Please do not include any confidential information in your communications. I encourage you to visit my website www.bhmklaw.com or call me at 513-579-1500 or 513-357-4328. Thank you for reaching out to me. Steve