Baird was born in Greenock on 16 November 1899 to David Baird, head of the science department at Greenock Academy, and his wife May. He studied science and medicine at the University of Glasgow, graduating with an MB ChB in 1922 and went on to receive an MD with honours. His early experiences attending births in the Glasgow slums and in the city's Royal Maternity Hospital shaped his interest in the social and economic influences on the health of women, their babies, and across generations. He was awarded Fellowship of the Royal College of Obstetricians and Gynaecologists in 1935.