You live in Mianyang, you can buy a car in Chengdu and drive back to Mianyang to get a license. However, it should be noted that if you want to buy a car, you must first write a formal invoice, buy a compulsory insurance in Chengdu and ask the car dealer to provide a temporary license plate. Now many 4S in Chengdu are authorized to open temporary license plates. As long as you have these procedures, you can drive back to Mianyang to get the license plate. If you get the license plate, you can complete the formalities on the same day and get the license plate in a week. This car is any 4S in China.

Further reading: How to buy insurance, which is good, and teach you how to avoid these "pits" of insurance.