In “Hadestown,” trombonist Brian Drye appears on stage and interacts with the cast. (As one theater observer noted on Twitter: “Phenomenal cast and all, but the trombone is the real star.”) In “Chicago,” trombonists Bruce Bonvissuto and James Burton III have coveted places on stage with the rest of the orchestra. “We can feel very viscerally the energy coming from the audience,” says Mr. Bonvissuto.

Then, there’s Mr. Boschen in “The Music Man.” “This is probably the coolest trombone part I’ve ever gotten to play” on Broadway, says the 48-year-old journeyman, who has performed with about 40 productions in a career that includes shows both familiar (“Cats”) and forgotten (a musical adaptation of Aristophanes’ “The Frogs”).

“The Music Man,” starring Mr. Jackman, a beloved take on Midwestern life circa early 1900s, is all about the band. Its key numbers include a homage to all things brassy—namely, “Seventy-Six Trombones.”

The production actually features two trombonists—Mr. Boschen, who plays the common tenor version, often simply referred to as the trombone, and Jack Schatz, who plays the bass version. Mr. Boschen jokes, “We’re 74 trombones short, but we’re trying our best to make up for it.”

Other tunes let him play in a jazzy or more romantic vein. He stays in the pit, but his presence is constantly felt.

Typically, trombonists have played supporting roles “like an offensive lineman,” says Mike Davis, a trombonist with “Moulin Rouge! The Musical.”

Producers have been reducing the size of Broadway orchestras as a cost-saving measure. Long gone are the Golden Age days when 25-piece ensembles were the norm, anchored by sizable string sections. Now, some shows can rely on 10 or fewer musicians—with digital instruments and tools often used to replicate the real deal.

But it’s hard to replicate a trombone, or “bone,” as it’s called in industry parlance, with its signature sliding sound. Also, the trombone is an instrument that adapts particularly well to many genres. “It’s good for so many things,” says veteran Broadway orchestrator Jonathan Tunick.

Mr. Boschen, a native of the Philadelphia area, has been wedded to his trombone since he picked up the instrument in third grade—it was either that or the cello, since both were suited to his height. He went on to study with trombonists in the Philadelphia Orchestra and then trained at the Eastman School of Music in Rochester, N.Y., and the Juilliard School in New York City.

He could have looked for a full-time job in a symphony orchestra, but decided he liked the varied life of a New York freelancer, where the gigs can range from playing jazz standards at a cocktail party to performing with classical ensembles, sometimes within the space of a day. A Broadway job is a coveted base, especially if it’s in a show that has potential for a decent run.

Mr. Boschen got his first shot as a substitute in “Cats” in 1997 and his first full-time position in “The Full Monty” in 2000.

Last July, while teaching one of his trombone students at his home near Peekskill, N.Y., he got a text telling him to call about “The Music Man.” He phoned and was told he had the job.

“He knows how to make something a comic moment or make it a jazz moment. It’s an art to what he does,” says Patrick Vaccariello, music director and conductor of “The Music Man,” who worked with Mr. Boschen on previous shows.

Like many Broadway musicians, Mr. Boschen is willing to play other instruments, if needed. Over the years, he has doubled on bass trombone and euphonium in shows, though he says he has a strict “no tuba” policy. “I’d rather be really good with less stuff than decent at more,” he says.

At “The Music Man,” Mr. Boschen shares an area the size of a modest suburban living room with about a dozen other brass and woodwind players (string musicians are in a separate spot). He is always mindful about where he aims his slide. During another show, he worried about knocking down the conductor’s podium.

“It would have been a showstopper in a different sense,” he says.

Mr. Jackman calls Mr. Boschen a “spectacular trombonist.” The actor, best known for his role as Wolverine in the X-Men cinematic franchise, says despite studying violin in high school he can’t fathom the skills required of playing in the pit. Mr. Jackman buys the musicians scratch-off lottery tickets every week in recognition of the valuable role they perform. Mr. Boschen says he’s won a couple of bucks so far.

“I have no business being down there other than delivering lottery tickets,” Mr. Jackman says, though he adds, “If there’s a part for a triangle player, I’m in.”

Pit musicians must contend with long stretches of a show where there’s nothing to do. Some text on their phones or do crossword puzzles during downtime.

On a recent Saturday matinee performance, Mr. Boschen kept busy reading a book on stock trading. He says he became interested in investing during the pandemic, when Broadway theaters were closed for months.

There’s always the risk of missing a cue to start resuming playing. Mr. Boschen says he internalizes the score so that rarely happens. The only time it did on “The Music Man,” he says, was when he got caught up in a moment hearing Sutton Foster, who plays Mr. Jackman’s romantic interest in the show, work her way through “Goodnight My Someone.”

“I lost myself in the beauty of the singing,” he says.

Mr. Boschen has never seen this production of “The Music Man” from the audience—nor does he plan to. That’s almost standard practice among Broadway musicians, who view their jobs as strictly focused on the score, not the broader production.

“I have my own version of the story playing itself out like a movie in my mind. I see it through hearing it,” he says.

Write to Charles Passy at [email protected]