Not sure if this is true....(and they didn't win Tonys) but I believe Nicole Kidman (The Blue Room) and Carla Guigino (After the Fall) had never even done a school play prior to their Bway debuts. If so I think they both did ok considering.
Whoopi (before anyone knew her) had a one woman show on Broadway in 1984 produced by Mike Nichols. This put her on the map. She was the new discovery and the thing to see. She won a Drama Desk Award and a Theatre world award for it. Then she did The Color Purple and the rest is history.
Tonys aside, in terms of stars who'd never done professional theater before appearing on Broadway, Jena Malone had never done a play at any time in her life before replacing Heather Goldenhersh in DOUBT.
Tonya Pinkins: Then we had a "Lot's Wife" last June that was my personal favorite. I'm still trying to get them to let me sing it at some performance where we get to sing an excerpt that's gone.
Tony Kushner: You can sing it at my funeral.