You may be able to tell the engine assembly date by looking at the left hand front of the block by the distributor at an extension used for attaching a water pump bolt. See pictures. The numbers are stamped into this extension by the inspector (or the assembly guy) in this format, 5H23Z: year - 5; month - H (January is A); day - 23; inspector - Z. The assembly date should precede the scheduled build date (from the door data tag) by at least a week (more likely longer). Post the car's VIN (use xx in the last two numbers for security) and we should get you close to that date.
Jim