The most likely explanation is that you just got the car loan and the lender hasn’t reported the information to any credit bureaus yet.
Another reason a car loan may not show up: you’re looking at the wrong report. Lenders report to TransUnion, Experian, and Equifax—or some combination thereof. If you’re only looking at one report, that might be the reason why you don’t see your car loan.
In other cases, an error may have occurred. But again, don’t worry. Credit unions and lenders will usually sort this out quickly. If you still don’t see the loan on your credit report after several months, contact your lender—and possibly the credit bureau—to address the situation.