It was Amber White’s second day as a stage manager on “Hamilton,” and Lin-Manuel Miranda, the show’s creator and star, was sick.

Viewers who buy their tickets months in advance are never happy to hear about a substitution. This was Broadway’s hottest show, based on a brick of a book by historian Ron Chernow, a fresh depiction of the New Yorker who fathered the American banking system, endured a sex scandal, and died in a duel. This was the first time that Miranda or Javier Muñoz, who plays the role on Sundays, didn’t appear as the title character. The role went to Jon Rua, the understudy, making his debut as America’s ten-dollar founding father.

White and the production team called an emergency rehearsal — 30 minutes long — for which the cast came to the theater. And then the show went on: “flawlessly,” White said, thanks to Rua but also the professionalism of the rest of the cast and crew.

White, 36, is one of the crew members in the room where it happens for eight shows a week, critical to the musical’s success but largely unseen.

Stage managers, three of whom work at a time on “Hamilton,” are the guardians and protectors of the show and the cast — “a cross between a flight attendant and a mom,” White says — who tend to the mental and psychological well-being of the actors.

They are also often with the show long-term, from pre-production meetings on design and concept through to rehearsals, previews and performances, taking care of the practicalities of scheduling and organization. And, always, troubleshooting.

During a recent production of “Hamilton,” an ensemble member hurt his neck with about 35 minutes left in the show.

Coming off stage, squeezing past barrels of prop rifles and shelves of neatly stored mugs, he went to the stage managers’ office to find White. The actor said he couldn’t go back on.

Quickly, White paged one of the swings — an understudy ready to fill in for multiple roles at a moment’s notice — upstairs in his dressing room. She and the other stage managers coordinated the switch, getting the swing into costume and microphone and on stage in time for his new character’s next appearance. The hurt actor went home.

The show went on. The audience never noticed. Crisis averted.