Galletta's first screenplay, Toy's House, was written as the thesis of his degree at Columbia University. In 2009, the script made the Black List, a survey of the best unproduced film screenplays, and was purchased by Big Beach Films the same week that the list was published, before Galletta had graduated from Columbia. The film was directed by Jordan Vogt-Roberts and renamed The Kings of Summer. It premiered at the 2013 Sundance Film Festival to positive reviews. Elements of the screenplay are based on Galetta's experiences as a youth living on Staten Island, but the producers of the film changed the location to Chagrin Falls, Ohio, a move that Galetta endorsed for giving the story "an 'any town' type of feel."

Galletta, who comes from an Italian background, grew up in Tottenville, Staten Island, New York, where he attended Tottenville High School. He graduated from the St. John's University College of Professional Studies; his major was in television and film studies. He later attended the Columbia University School of the Arts and graduated with a Master of Fine Arts in 2010.