I am back from a long day, so I am sure I am missing obvious ones, but the jazz guitarist **Stanley Jordan **- he plays with a wonderfully unique two-handed tapping technique - played on NY streets before he broke loose…
I could have sworn I read once that Lisa Gerrard was a busker in Australia before she met Brendan Perry and formed Dead Can Dance, but I can’t find a link anywhere.
I first heard of Billy Bragg as a busker, but his Wikipedia page says that he had a band beforehand. As is usual for record companies, they re-wrote his history to suit themselves.
Michelle Shocked is fairly unique in that she had a hit record without knowing she did, or even intending to release a record. Her album The Texas Campfire Tapes was a Walkman recording of her playing songs around a campfire at the Kerrville Folk Festival.