Answer by taking a quote from the following article:

Natalie McIntyre was born in Canton, Ohio, the daughter of Laura McIntyre, a math schoolteacher, and Otis Jones who left when she was a baby. Her stepfather was a steelworker, and she has a sister who would become a biology teacher. She began piano lessons at age seven. A childhood bicycle mishap resulted in her noticing a mailbox of a man named Macy Gray; she used the name in stories she wrote and later decided to use it as her stage name.

While attending the University of Southern California, she agreed to write songs for a friend. A demo session was scheduled for the songs to be recorded by another singer, but the vocalist failed to appear, so Gray recorded them herself.  I started forming bands and writing songs just for fun and then I really got into it and got attached to it. Then a friend of mine asked me to be a singer in his jazz band. He gave me all these jazz CDs and I studied all these different singers and I kind of taught myself how to sing for a gig, but I didn't take it seriously until later.  She then met writer-producer Joe Solo while working as a cashier in Beverly Hills. Together, they wrote a collection of songs and recorded them in Solo's studio. The demo tape gave Gray the opportunity to sing at jazz cafes in Los Angeles. Although Gray did not consider her unusual voice desirable for singing, Atlantic Records signed her. She began recording her debut record but was dropped from the label upon the departure of A&R man Tom Carolan, who had signed her to the label. Macy returned to Ohio but in 1997 Los Angeles based Zomba Publishing Senior VP A&R man Jeff Blue, convinced her to return to music and signed her to a development deal, recording new songs based on her life experiences, with a new sound, and began shopping her to record labels. In 1998, she landed a record deal with Epic Records. She performed on "Love Won't Wait", a song on the Black Eyed Peas' debut album Behind the Front.

How did Macy Gray start her musical career ?
Then a friend of mine asked me to be a singer in his jazz band.