Elsewhere on this board, there's a related discussion about this subject. In that thread, a fellow has a 2002 car, with a sticker stating production date of May 2001. It has been confirmed that GM started production of the 2002 model year unusually early (in May 2001, instead of the usual August) as the F-body would be ending production in model year 2002. Sounds to me like you have a very early build 2002 car.
Similarly, the 1990 F-body production run was unusually short, and 1991 production started very early, as GM wanted to get the 1991 notably restyled cars into showrooms early. So there is a precedent for your 2002 car being built in May of the previous year.