Galvin was born in the Sydney suburb of Woollahra, and was educated at Petersham Commercial School.

He then considered a tilt at federal politics, but was convinced by his friend, John Cain, to nominate for the 1945 Bendigo state by-election, triggered by the death of Arthur Cook.

Following the defeat of the Cain government in 1947, Galvin was elected deputy leader of the Labor Party in Victoria.

At the 1955 election, Galvin was defeated in Bendigo by the Liberal and Country candidate, John Stanistreet, by just twelve votes.

His defeat, preventing him from the running for the leadership of the Labor Party, and Shepherd was elected leader when Cain died in 1957.