The original Kingdom Hearts was released in North America in 2002.
More specifically, the PlayStation 2 game launched in North America on September 17, 2002. It was developed by Square and created through a collaboration with The Walt Disney Company, combining Disney characters and worlds with original characters and elements from Square's Final Fantasy series.
The Japanese release came earlier, on March 28, 2002. The North American version included additional content that was not in the initial Japanese release, including optional bosses, another difficulty level, and a teaser for a possible sequel. Some of that material was later incorporated into Kingdom Hearts Final Mix, which first launched in Japan in December 2002.
The game's success established Kingdom Hearts as a major franchise. It was followed by Kingdom Hearts: Chain of Memories in 2004 and Kingdom Hearts II in 2005 in Japan. The year 2002 refers specifically to the original game's North American debut, not the later releases or the Final Mix edition.