I think Audiograbber was the first popular program to rip MP3's from your CD collection. Best I can tell, it was first released as v1.41 in Feb 1997. Winamp came out a couple months later.
And then young people were absolutely listening to their CD's as MP3's on their computers by the summer of 1997 -- I know I was, it was just so much more convenient. And you definitely didn't need to wait for Napster if you were on a college campus with dorms -- you'd find tons of "anonymous" network shares filled with thousands and thousands of tracks in the fall of 1997 for sure.
And the Diamond Rio player came out at the end of 1998... I remember that was huge... all of a sudden your MP3's were portable!