Goodwyn was born at Roorhir, Bengal, in British India (now Ruhea, Bangladesh).
En route to the final, the Engineers did not concede a goal and defeated Hitchin 5–0, Hampstead Heathens 3–0 and Crystal Palace 3–0 (after a goalless draw).
Although the Engineers entered the final, played at Kennington Oval on 16 March 1872, as "favourites to win the trophy",[4] their opponents, the Wanderers, won the match 1–0.
He was selected for the second official international match between England and Scotland played at Kennington Oval, London on 8 March 1873, together with his Royal Engineers colleague, Pelham von Donop who played alongside him in defence.
In its report on the match, the Glasgow Herald (Monday, 10 March 1873) noted that "the back play of A G Goodwyn ... was faultless".