Organized music piracy (mp3 scene) began in the summer of '96 when 3 of the major groups were formed (of which RNS was the most famous and long-lived). By '97 it was 'adopted' by the software (warez) scene, and also borrowed its supply and distribution chains--there was now competition for having the fastest releases, as well as means for getting these ahead of official release dates--precipitating popularity.
According to mp3scene.info, there's was mp3 piracy on usenet as early as '95.