Could a film be engineered so it achieves immediate cult status for its absurd qualities, transgressive elements, and slapdash manner of storytelling? The new movie “Problemista” certainly seems to aim for such notoriety as it loops around the story of a Salvadoran immigrant and his potential art critic sponsor. 

Hilarious, shallow, irreverent, and inane, the movie affects a daffy, farcical tone despite a seriousness that edges in at times. 

Named Alejandro, our hero begins the movie as a kid living in a fantastical jungle setting protected by his doting mother, before we find him in the present day as a young man at New York City. An aspiring toy designer, Alejandro works at a cryogenics firm that freezes artists who have terminal illnesses and/or wish to wake up later in a future world. 

After a mishap, Alejandro loses this job and the company’s sponsorship of his work visa. So begins Alejandro’s month-long odyssey — fraught with the occasional glimpse of an ever-running hourglass — to secure a new employer willing to sponsor him.

The new employer comes in the shape of a cantankerous, chaotic art critic named Elizabeth. Before being fired from his job, Alejandro was not only the overseer of her late husband Bobby’s encapsulated body, but also the archivist of his personal effects and paintings. Intrigued by Alejandro’s helpful demeanor, she offers to take him on as an assistant and eventually sponsor him should he prove industrious. 

Soon, he’s not only helping her sort out her technologically clueless life — there’s a running gag about her reliance on FileMaker Pro — but also planning an exhibition with her of Bobby’s artwork, all of which feature eggs.

The first 30 minutes or so of “Problemista” present several “problems” for the average viewer: arch narration from Isabella Rossellini, an almost dopey protagonist, a haranguing deuteragonist (later tritagonist), a strange editing cadence, and humor that feels both obvious and labored, as in the cryogenics scenes. Even Alejandro’s toy ideas, such as a Barbie doll with one of her hand’s fingers crossed behind her back, fall flat as jokes. 

Remarkably, though, these same elements start to weave together after the first half-hour, not exactly seamlessly but affectionately, with one growing fond of Alejandro’s cockeyed perspective and Elizabeth’s confrontational aspect. Beyond reason, we begin to root for these two seemingly mismatched curatorial partners to succeed in rounding up 13 of Bobby’s egg paintings. 

Among the movie’s disparate intentions is to address the daunting intricacies of American immigration policy and basic city survival. Writer/director and lead actor Julio Torres, though, is not content to portray Alejandro’s quest for a work visa merely pseudo-realistically. He also films fantasy sequences in which he plays Alejandro as a knight and Elizabeth is a dragon. Likewise, the character’s interim efforts to find cash-paying employment are depicted both matter-of-factly and surreally, with vignettes of Alejandro’s forays into menial jobs envisioning Craigslist as an apocalyptic cesspool complete with a troll-like attendant. 

Alejandro’s story isn’t so much an adventure as it is an anxiety-ridden funhouse. Mr. Torres even illustrates Alejandro’s navigation of immigration law and rules as an impossible structure/optical illusion of rooms arranged precariously on top of other rooms, with no way into the one room in which legal status is established.

Most of these flights of fancy help flesh out Alejandro’s plight while keeping the film’s tone lite and arty. For truly, if one examined its characters and narrative, one would deem Elizabeth an elitist “Karen” and Alejandro’s story a discouraging, unconvincing one. 

As an actor, too, Mr. Torres keeps things playful with his slight lisp, bouncy walk, and that one flyaway lock of hair sticking up from his head like a sagging antenna Dali might have painted. Sometimes it seems like he’s channeling a bit of Charlie Chaplin, at other times Jacques Tati, yet there’s no denying the comedian has a persona all his own.

It is Tilda Swinton as Elizabeth, though, who makes the movie more than a curiosity but a must-see. As she rants and raves in a West Country rural accent throughout, she also, miraculously, taps into the character’s aching need and loneliness. Indeed, the renowned actress brings such manic but precise comic timing to her lines that one wishes she would act in more movies that didn’t require her to play withdrawn and distinguished. 

By the film’s end, themes of friendship, struggle, and the purpose of art are rendered in a rather simplistic, almost sitcom style, while others baked into the plot, like guilt and regret, go largely unexplored. Still, with his first feature, Mr. Torres proves that a weird energy, scrappy script, and unusual performances go a long way in establishing one’s outré bonafides.