At one time, before the DeLorean factory closed, the factory undoubtedly had a "Master Record" of all the cars that had been manufactured with all the details they felt important to keep - VIN, engine and transmission serial numbers, key codes, and start/finish assembly dates.
Over the past 30+ years since the factory closed, only limited records have been discovered. When DMC (Texas) acquired the remaining parts that came from the factory and US-based warranty parts centers, various documents were discovered that contained some of this information.
All of these documents were loaned to The DeLorean Museum, a non-profit corporation, and they have sorted, arranged and cross-referenced this data and other data they have acquired from former DMC employees and others into a database encompassing more than 6,000 or so of the 9,000+ cars produced.
For more details, visit the Museum website.