Actually no. Navies train along time with their new ships prior to going on deployments. Usually these crews came from other similar class of ships. For example, the USS George Bush, the USN's newest carrier is more or less the same as any other Nimitz class carrier but it took awhile before the Bush was ready for pre-deployment training exercises.
Even using the TNG technical manual, even though the highly quoted 20 year figure doesn't completely show truly how long it took the Galaxy class ship to be built. Off hand, I think it was five or six years which falls in line with a ship of that size. Later on let's say before the Dominion War, they could have reduced it down to 3 years.







