You can get a smog check without having your DMV renewal notice.
The smog technician needs your vehicle's VIN (vehicle identification number) in order to record the inspection results and upload them to the DMV. The smog technician can get the VIN from multiple locations off your vehicle; for example the public VIN located on the lower left side of the windshield, the VIN printed on the center post (driver's side door jam), or any registration document (expired or current) which indicates the vehicle's VIN number.