A big-spectacle Broadway production is, quite visibly, a collaborative effort — actors, sets, choreography, costumes, lighting, orchestra. On rare occasions, though, beneath the razzle-dazzle, a major Broadway show can also represent the singular expression of an artist’s voice, one that speaks to an audience so directly and powerfully that watching it, you feel as thrillingly enveloped in the soul of that artist as you do when standing in front of a Jackson Pollack painting or reading a novel by Jane Austen. The artists of Broadway who achieve that level of intensely personal yet mythological force come along once or twice in a generation. Michael Bennett did it with “A Chorus Line.” Tony Kushner did it with “Angels in America.” And Lin-Manuel Miranda did it with “Hamilton,” the exhilaratingly brash historical hip-hop musical that has done nothing less than rewrite the way Americans think and feel about the Founding Fathers, getting us to see them with new eyes: not as plaster headstone saints but as the furious and complicated gangsta idealists they were. As history, as recontextualized racial fusion, as the cutting edge of theater in the 21st century, “Hamilton” is more than an event — it has been a revolution.

So it’s extraordinary to see Lin-Manuel Miranda, a full two years before the show’s opening night, in the early moments of “Hamilton’s America.” The movie is an intoxicating documentary about the creation of “Hamilton,” and here’s Miranda, 33 years old, standing in the Washington Heights apartment that he and his pregnant wife have spent most of a year renovating (they still can’t move in), his life in total flux, talking about how much of “Hamilton” he has written so far: exactly one song. It’s not just that the show isn’t finished yet — or that no one, including him, has any idea of the phenomenon it will turn out to be. It’s that Miranda barely even knows what the show is. What he has is a vision, a feeling, an instinct that has come from the flash of lightning in his brain.

Miranda, as “Hamilton’s America” reveals, is a creator of genius ferocity who nevertheless has a disarmingly sweet spirit. With his long hair and goatee and big glistening dark eyes, he looks like a softer, puppy-dog version of Al Pacino in the ’70s, without that haunted quality that Pacino had from the moment he showed up in “The Godfather” and never really lost. If Miranda has demons, they aren’t visible. He’s got a gregarious smile and a bright, warm, open-for-business charisma, to the point that you may wonder, at first, where a fellow this easygoing keeps the extraordinary audacity that fuels each and every moment of “Hamilton.” Where that comes from, I think, is that Miranda, in his nice-guy way, gives off a glow. There’s a light of insatiable eagerness inside him.

He talks about the genesis of the show: how he was on vacation, looking for something to read, when he plucked Ron Chernow’s 2004 biography “Alexander Hamilton” off a shelf virtually at random. (There’s a casual snapshot of him reading it on the beach that, in hindsight, is so epochal it gives you chills.) And he describes what he felt — or, more to the point, the radical insight he was hit with. He saw how people like Hamilton and Aaron Burr, with their deep shared faith in the experiment of America but their head-butting (and pistol-crossing) disagreements and rivalries, were in many ways like Biggie and Tupac. They were on fire with their words and beliefs, and with their conflicting versions of what those beliefs should lead to. But, of course, telling the story of one of the Founding Fathers in hip-hop rhyme isn’t something that can be rationalized, or entirely explained. It was an epiphany, an aha moment. Miranda just saw it, and right there he knew: This would be his next musical.

In “Hamilton’s America,” we see him writing the early numbers of “Hamilton” on his laptop while he’s still doing eight performances a week of “In the Heights,” his breakthrough musical (for a while, the pace of his “Hamilton” songwriting was one song per year). Then, in the moment when it all blew up, he was engaged to perform a number from “In the Heights” in Washington, D.C., for an audience that included the Obamas, and he took the chance to debut the one and only “Hamilton” rap he had written. It was a sensation, and — famously — a clip of it went viral on YouTube. The show didn’t even exist yet, but already it was off and running.

What made that clip so special? I think it had to do with the way Miranda’s age gave him a revelatory angle on hip-hop culture. In “Hamilton’s America,” there are several occasions when we see him free-styling, most spectacularly during the closing credits. Standing backstage, he tosses off a rap of such savage density and insouciance, and makes it look so easy, that we’re awed by his gift. It may be fair to say that Miranda, although the category he exists in is “Broadway showman,” is one of the five or six most virtuoso MCs in the history of hip-hop. Yet he came along significantly later than the gods of the form. Miranda was born in 1980, making him roughly a decade younger than Nas, Biggie, Jay-Z, Eminem, and the other wizard rappers he grew up listening to, so even more than Eminem, the original cross-cultural rap superstar, he inherited hip-hop as a form that seemed to him to have existed forever. Which is why he could twist it in entirely new directions. To Miranda, it wasn’t a form to bow down to — it was a form to be used.

“Hamilton’s America,” in capturing that journey, turns out to be a thrillingly nimble and moving testament. The movie, which features enough of the show to let you relive it (or, if you haven’t seen it, to whet your appetite), will air on Oct. 21 as a PBS “Great Performances” documentary, and there’s every chance that it could set some sort of viewership record. But whether it does or not, there are many thousands of people who will find it immensely gratifying to see all the ways this film heightens and enhances their original experience of “Hamilton.” In a fleet and shapely 84 minutes, it manages to avoid every cliché pitfall of the standard behind-the-scenes making-of documentary.

The director, Alex Horwitz, was a college buddy of Miranda’s, which is why Miranda trusted him enough to give him access to the process. But if that makes it sound like the film might take too gauzy a view of its subject, what Horwitz has done is to craft a movie of privileged moments that reveals the creative process with stubborn insight. He shot 100 hours of footage over the course of three years, yet he had the discipline to whittle it all down to a film that includes (for instance) no rehearsal footage. Horwitz must have realized that when you’re watching people rehearse a musical in a studio, whatever the show happens to be, it always has the same “All That Jazz” backstage vibe of “five-six-seven-eight!” diligence.

In place of scenes like that, “Hamilton’s America” digs deep into “Hamilton” itself, and into what Miranda discovered as he was creating it. There’s an arresting diversity to the film’s interview subjects, with some of the interviews conducted by Miranda himself. He talks to Stephen Sondheim and John Weidman, whose political musicals (like “Assassins”) were door-opening inspirations to him, and also to Nas, and to President Obama, whose imperious joviality expresses his own slant on why the Founding Fathers still rule. Beyond that, the movie elicits fascinating testimony from artists like Questlove, who describes how he had to see “Hamilton” eight or nine times to absorb all its levels of meaning, and from political figures like Elizabeth Warren, who offers an exuberant pinpoint analysis of how Hamilton basically invented our financial system, and even George W. Bush, who comes across with more empathetic intelligence than I have ever seen him display.

“Hamilton’s America” captures every stage of how the show exploded as a cultural phenomenon: its triumphant move from the Public Theater to the Richard Rogers Theater on Broadway (where crowds pack the streets as if gawking at royalty), its entrance into popular culture with the aid of bedazzled fans like Jimmy Fallon, and its arrival at the White House, where Miranda and company give a plain-clothes performance heralded by a visibly ecstatic Michelle Obama. At every stage, we register how “Hamilton” is the rare musical that wasn’t just of its time but ahead of it. The casting of African-American and Latino actors to play historical characters we think of as lily-white was, of course, central to the musical’s mystique. Yet that gambit would have taken Miranda and company only so far if the show itself wasn’t embedded with so many head-spinning layers of the immigrant mythology of America. Those layers tingle with meaning as you watch “Hamilton’s America.” Hamilton himself was, of course, a besieged orphan who came from the Caribbean island of Nevis. Miranda’s father arrived from Puerto Rico (an American territory, but a different world), and Miranda himself was born and raised in New York City, growing up as a casually assimilated Latino-American — the proverbial happy ending to the eternal immigrant saga, right?

Except that wasn’t the ending. As an American, someone with the freedom to dream in new ways, Lin-Manuel Miranda immersed himself in two forms that, only 20 years ago, would have seemed oxymoronically dissimilar: the world of Broadway and the world of hip-hop. Rap was an African-American form until the Beastie Boys pranked their way inside it, followed by Eminem, who rose up to declare, for the first time, that a white dude could work in this form with a level of intensity and brilliance that rivaled that of its greatest artists. At that point, hip-hop still had its outlaw/rebel/street allure. But then along comes Miranda to say, in “Hamilton”: This is not a “street” form, or even a youth form — this is an American form, pure and simple. It retains its rebel fervor, in its every aggressive thrust and off-the-top-of-your-brain declaration, but that’s what makes it American; we were born as rebels. Hip-hop turned out to be the perfect form to channel the voice of the Founding Fathers because it already is their voice: an echo, down through the generations, of what it means to make up your destiny one line at a time. What Miranda did in “Hamilton” was to reclaim the way that Alexander Hamilton and company, before they were anything else, were writers — and (to a degree scarcely acknowledged by educators) that they were improvising. The brilliance of the show is that it uses the idiom of hip-hop to place the nuances of their thoughts center stage.

One commentator in “Hamilton’s America” likens Miranda to Shakespeare, pouring history into a popular form, with the twisty spoken word of hip-hop standing in for iambic pentameter. That may be the film’s key takeaway, because whether or not you agree, it’s a thought — or maybe a debate — you totally want to have. Is “Hamilton,” as a work of art, worthy of comparison to Shakespeare? Discuss! What’s undeniable is that Miranda, in channeling the spirit of the American Revolution, created a revolution on Broadway. “Hamilton’s America” puts you backstage — and center stage — at the moment when he turned pop culture upside down.