McGinty was born in Orange to Laurence Russell Leonard McGinty and Ellen Margaret Elizabeth Magee. He was educated at Christian Brothers High School at Lewisham and St Joseph's College at Hunters Hill before studying at the University of Sydney, where he received a Bachelor of Laws in 1944, having worked as an assessor for the Taxation Department from 1939 to 1942. He enlisted in the army in 1942, shortly afterwards transferring to the Royal Australian Navy, eventually becoming a lieutenant. After his return he was a legal officer with T.S. Skillman and Company from 1947 until 1955, when he was admitted as a solicitor. He was elected to Willoughby Council in 1957 and was Mayor from 1960 to 1967. He was also active in the local Liberal Party.
