“Supergirl” is a very good, polished pilot, which, in TV terms, might be one of the least interesting questions hovering around this latest DC Comics adaptation from producers Greg Berlanti and Andrew Kreisberg. The introductory hour hews closely to that pair’s formula for “The Flash,” from elevating an adorable “Glee” alum (there Grant Gustin, here Melissa Benoist) to costumed-icon status, to the it-takes-a-village approach to raising a superhero, with plenty of people in on the character’s secret virtually from the get-go. All that, however, belies the main issue: Can such fare fly on CBS?

“The Flash,” of course, has been a major hit by CW’s less-demanding standards, which perhaps emboldened its older half-sibling to take a flyer (heh heh) on its own bold comics-to-TV leap. Never mind that the Marvel name hasn’t produced major ratings for ABC’s “Agents of SHIELD,” although the brooding “Gotham” did emerge as a solid contender on Fox.

Still, for CBS, immersed as the network is in crime procedurals, “Supergirl” represents a sizable gamble. And while some of the pilot’s accessories seem designed to address those concerns — most notably Calista Flockhart as the central character’s imperious media-mogul boss, Cat Grant, giving the show a “Devil Wears Prada” vibe — ultimately, the network is hoping there’s a wider audience, relatively speaking, than tuned in for its version of “The Flash” a quarter century ago.

On the plus side, Benoist nails the title role — a name, incidentally, that is quickly explained away, seeking to deflect any charges of sexism about the “girl” designation. In a rapid-fire origin story, it’s explained that Kara was the older cousin of Kal-El/Superman, who exists (mostly for legal/DC continuity reasons) in an unseen part of this show’s world.

On her way to Earth, however, Kara got sidetracked and spent 24 years in the Phantom Zone, which explains why she’s younger than her better-known relative. Now in her mid-20s, she stayed anonymous for more than a decade, growing up with an adopted sister (Chyler Leigh) who is eager to protect her — and her secret.

Naturally, events force Kara to show off what she can do, and she does so spectacularly, in a plane rescue that vaguely echoes the original Christopher Reeve “Superman.” As in that movie, there’s a sense of exultation in the early scenes in which Kara explores her powers, after spending so many years trying to blend in and be “normal.”

Taking a page from “The Flash” and “Smallville” before it, the series also seeks to establish via Kara’s origin tale both a deeper mythology and an excuse for Earth to be populated by various super-beings, giving her someone to pick on, as it were, who’s at least close to her size, power-wise. Between that and establishing her network of friends, that’s a whole lot of business to cram into an hour, raising the age-old question of how the series will fare on an episodic basis, once it lacks the kind of budget that would make most independent films the color of Kryptonite with envy.

Good casting (including Mehcad Brooks as Superman’s pal Jimmy Olsen — now hunky, African-American and going by the grown-up moniker James) and Benoist’s deft handling of her dual role create hope for the show going forward. So does the manner in which the producers and Warner Bros. have generally sustained the level of special effects and action on “The Flash.” Once again, there are also nice homages to the past, such as Dean Cain and Helen Slater as Kara’s adoptive parents.

That said, this is still a considerable gamble for all concerned, and an enthusiastic response from comic geeks alone won’t be enough to propel “Supergirl” into the sort of orbit CBS will need — even in an age of diminished expectations — to justify this dice roll. (In a shrewd move, the network is leveraging its most popular geeks, “The Big Bang Theory,” to help its fellow Warner Bros. Television offering achieve liftoff.)

On the plus side, finding the right star, and constructing a credible pilot, are big parts of the battle. Thanks to those strengths, if the producers can sustain the playfulness and action without going overboard on Flockhart’s character, there’s reason to believe this “girl” can fly.