Before starring on The Real O'Neals, he also appeared off Broadway at theaters such as the Signature, Playwrights Horizons, MCC, The Vineyard, The Public, The Culture Project, The Flea, The Wild Project, New York Theater Workshop, the Barrow Street Theater, Rattlestick, Ensemble Studio Theater, and many others. He is a recipient of Audio file Magazine's Earphones Award for his narration of Hollis Seamon's novel Somebody Up There Hates You. His other audiobook work includes Perks of Being a Wallflower, Matthew Quick's Forgive Me, Leonard Peacock, and more. Additional credits include the celebrated short films Promised Land and Welcome to the Wayne.
In August 2017, Galvin was named as a temporary replacement for the title role in Dear Evan Hansen after the departure of Ben Platt. Galvin assumed the role on November 21, 2017 and played his final performance on February 4, 2018.