Goodwin was educated at Sydney Boys High School and represented Australia at the International Chemistry Olympiad in 1996, winning a gold medal.
Goodwin earned a BSc in chemistry and pure mathematics at University of Sydney (USYD) in 2002. He completed a Ph.D. in inorganic chemistry at USYD in 2004 under advisor Cameron Kepert. Goodwin earned a Ph.D. in mineral physics from University of Cambridge in 2006 under advisor Martin T. Dove. He was a junior research fellow at Trinity College, Cambridge from 2004 to 2009. Goodwin was a visiting fellow at the Australian National University in 2007.