McCay was born on 21 December 1864 in Ballynure, County Antrim, Ireland, the oldest of ten children to the Reverend Andrew Ross Boyd McCay, a Presbyterian minister, and his wife Lily Ann Esther Waring (née Brown). The family emigrated to Australia in 1865, settling in Castlemaine, Victoria. Boyd McCay continued his theological studies while he was a minister in Castlemaine, earning a Master of Arts (MA) from the University of Melbourne in 1882 and a Doctor of Divinity from the Presbyterian Theological Faculty Ireland in 1887. Esther could speak seven languages. The two separated in 1891.