How soon will a new car purchase show on your credit report?

The purchase of a car is not shown on a credit report. The only item that might show would be an account wherein a consumer borrowed money secured by a car. If no money was borrowed, there would be no listing. If a loan was obtained, whether or not the loan shows on your CR would be at the discretion of the lender. Some lenders are members of various Credit Reporting Agencies, some are not.