I believe Phil Spector started his musical career in a doo-wop vocal group called The Teddy Bears (big hit "To Know Him is to Love Him").

Paul Simon and Art Garfunkle recorded Everly Brothers style duets as Tom and Jerry when they were teenagers.

Bob Dylan played harmonica (very well) on an album by Carolyn Hester before he ever recorded under his own name.

Jack Bruce started out playing stand-up bass in a dixieland group called Jim McHarg's Scottsville Jazz Band.

Alan Lomax and Shirley Collins were both members of a skiffle group called The Ramblers.

Nic Jones sang in a group called The Halliard before achieving greater renown as a solo artist.

John Kirkpatrick began his musical career playing piano-accordion for Hammersmith Morris Men.

John Renbourn played in an R&B band called Rupert Hogsnort and His Famous Porkestra before making it as a singer-guitarist in his own right.

And there must be more ... but I can't think of any at the moment.

Wassail!