The Creators of Crash - Josh Mancell
The music for the original game was created very late into development. Even long after it was playable and most of the final concepts were entering their finishing touches, the levels were silent asides from the sound effects caused by Crash and the other characters.
Jason Rubin eventually left a note to the game's producer, Dave Siller, regarding this issue. The latter interviewed Mark Mothersbaugh, a musician who co-founded the music company Mutato Muzika. The interview went well and Dave loved the samples they provided him.
The music was composed by Josh Mancell, an in-house composer at Mutato Muzika. According to him, Mark thought he would be a good fit for the Crash project. His judgment turned out to be spot on, as Josh's music was lauded by fans and critics alike, and he was brought back for all of Naughty Dog's games up to and including Jak 3.
In an interview with Josh, he recalled that creating music for the series was a smooth process, and he would often visit Naughty Dog to play some of the levels they were working on in order to get a general idea of what to compose. Various tribal and Australian instruments (such as the didgeridoo) were used prominently, and as the games became more expansive, so did Josh's soundtracks.
Due to the PlayStation's limited hardware, there were things he would have liked to do with the music that weren't possible. Though he wasn't particularly keen on the quality of the final mixes produced by the PlayStation, his involvement became heavier after the first game, ensuring that it had the least downgrades possible.
These days Josh Mancell can sometimes be found posting the original pre-console mixes of the Crash Bandicoot music in his SoundCloud page as a fun way to revisit the past and bring the fans something more to enjoy.