McNair was born in Kingston, Jamaica. He started out at the Alpha Boys School under the tutelage of Vincent Tulloch, while playing with Joe Harriott (a lifelong friend who considered McNair his de facto younger brother), Wilton "Bogey" Gaynair, and Baba Motta's band. He spent the first decade of his musical career in The Bahamas, where he used the name "Little G" for recordings and live performances. His early Bahamian recordings were mostly in Caribbean musical styles rather than jazz, in which he sang and played both alto and tenor saxophone. He also played a calypso singer in the 1958 film Island Women. In 1960, he went to Miami to record his first album, a mixture of jazz and calypso numbers entitled Bahama Bash. It was around this time that he began playing the flute, which would eventually become his signature instrument. Initially he had some lessons in New York, but he was largely self-taught. He departed for Europe later in 1960.