It actually started a long time before that.
FF1 had the then-traditional "build party out of a set of classes" approach to party construction that was popular in Western RPGs like Dungeon Master or Ultima. It also used the "sprawling overworld / dungeons" approach that Ultima liked. It just added a Japanese sensibility and blended in some ideas from Dragon Warrior that made for a good fusion that everyone liked.
FF2 added the idea of a rotating cast of core characters who each had their own story and specialties, which set the tone for the rest of the series. It also experimented with a wild new experience system, which did not work out and was never revisited.
FF3 actually added the class system that 5 later improved on (dramatically), and created a few of the "appear in every game" characters.
