The same company who recorded Debussy also recorded Grieg, Massenet and Pugno (whom I've never heard of before) in 1903: these recordings are now avaiable on CD: see here for a track listing.

Things may not go back much further than that. This article argues that gramophone recording only took off seriously from 1901-2 with the introduction of wax masters which improved quality, and the first recordings of Caruso which brought the concept to a wider audience.