Sometimes it shifts out of park right away.
My car takes about two to four minutes before you can shifts out of park on 1999 Buick Regal
Start by having a transmission flush done with a new filter, then use Dexron VI to fill. If the problem persists, have a professional transmission shop scan the transmission for codes and perform a pressure test. Is the problem that the shifter doesn't move, or the shifter goes into drive but you have to wait for it to start moving?
Have a mechanic check the shifter interlock! Possibly just contaminated and needs cleaning.