the sticker on the door gives the month/yr.
But yes- with the VIN - someone can look it up (dealer) and can tell you the exact day it was built.
see my signature below- I know the exact day mine was built. to me that date is significant- why?
because that is the day AFTER- that Spring Hill came back up to production when they started building the 2010's. (after GM idled many plants because of the bankruptcy-economy).
(also one of the reason my vehicle was pulled off the line and had tests run on it).