Its characters may have those same googly eyes and four-fingered hands, but it’s obvious from the get-go that “Futurama” ain’t “The Simpsons” — Matt Groening pedigree or no Matt Groening pedigree. But it pays to remember that at the beginning, “The Simpsons” wasn’t yet “The Simpsons,” either. True genius sometimes takes time to develop. And while this sci-fi spoof saunters onto the Fox midseason sked feeling a tad uninspired at first blush, the promise is clearly there, particularly if we’re using the overzealous, overhyped “Family Guy” as a basis of comparison.

The joke in “Futurama” is that it’s 1,000 years in the future, New Year’s Eve 2999, where a hapless 25-year-old New York City pizza delivery guy named Fry (voiced by “Ren & Stimpy” vet Billy West) finds himself after leaping ahead a full millennium, courtesy of a cryogenic time-freeze tank in which he became accidentally trapped. When he awakens, Fry — whose limited brain capacity calls to mind a younger Homer Simpson — notes that everyone he ever knew has been dead for roughly 950 years or so, leaving him somehow giddy.

It turns out that the future has not been particularly kind to New York. Everything — including the Statue of Liberty — is now underground, the city’s skyline made over by aliens following their successful invasion some centuries before. The Angelyne billboards remain (that woman truly is ageless), but the main jetway is now called JFK Jr. Airport, and the subway has been replaced by a pneumatic tube through which one whooshes solo before crashing into a wall.

No need for Dr. Jack Kevorkian in the 31st century, either: The streets of Manhattan are dotted with a series of Suicide Booths. For a mere 25¢, the hopelessly depressed can enter a small unit and choose their mode of demise — “quick and painless” or “slow and horrible.” At the conclusion, a friendly recorded voice utters the useless message, “You are now dead. Thank you for using Stop & Drop.”

This is easily the most wickedly amusing gambit in the uneven “Futurama” pilot, penned by exec producers Groening (who is also listed as the show’s creator) and David X. Cohen. They paint a future in which comely Cyclopes and surly robots have managed to blend seamlessly with the human citizenry, and where the disembodied heads of long-dead celebrities such as Leonard Nimoy, Dick Clark and even Matt Groening himself have been preserved in museum glass.

As Fry stumbles into the year 3000, he is accosted by Leela (Katey Sagal), a sassy one-eyed female alien with understandable depth-perception problems. He also links up with Bender (John DiMaggio), a smoking, boozing kleptomaniac of a robot who wants very badly to kill himself, if only his hard metal shell would allow it.

Anyway, the future requires people to be implanted with a “career chip” that forces them to adhere to one employment assignment for life. Those who refuse are fired out of a cannon into the sun. Fry nonetheless rejects his assignment of Delivery Boy until he realizes that he can go to work for a company that hustles packages to “all five quadrants of the universe.” As the opener ends, he, Leela and Bender have shoved off together on their first mission as an interstellar messenger service.

OK, so this ain’t exactly knee-slapping material — yet. It isn’t even quite the “Jetsons With Attitude” that we might have expected. But the animation is richly textured, and there are enough irreverent sight gags and wiggy asides to paint this as a “Simpsons”-inspired enterprise that doesn’t pander. Groening continues to make good on his promise to reward viewers who pay attention on a dial where the predominant payoff is drowsiness.

Fox executives already appear to have cast their vote on “Futurama,” however. Following two special Sunday airings at 8:30 p.m., the show gets demoted to Tuesdays following “King of the Hill,” while the nutso farce “Family Guy” snares the coveted post-“Simpsons” slot for the whole of its spring trial run after having launched in back of the Super Bowl.