Almost paradoxically, a theater set designer’s work is most successful when, in a sense, it is invisible. When a set seems to somehow spring from a play so organically that the audience’s imaginations can be transported anywhere. Set designers are like backstage magicians, and yet the vast majority of theater fans would probably be unable to name a single one. Well, here’s one to remember: Mariana Sanchez. A native of Mexico, Ms. Sanchez lives full time in Amagansett with her husband and their 4-year-old daughter (they recently bought and renovated a house in Springs). Her onstage craftsmanship can be seen in “Marys Seacole,” a critically acclaimed play now at the Claire Tow Theater, Lincoln Center Theater’s newest space and home to LCT3, the company’s initiative dedicated to producing the work of new artists. Written by Jackie Sibblies Drury and directed by Lileana Blain-Cruz, the tragicomedy about Afro-Caribbean caregivers tending to white patients features an all-female cast and creative crew. Several critics have noted Ms. Sanchez’s artistry. Ben Brantley of The New York Times reported that her set “morphs from what appears to be a modern, pink-walled hospital into the Jamaica of Seacole’s childhood and, hilariously gruesome, a bloody Crimean battlefield.”And in a New York magazine review: “Into Mariana Sanchez’s antiseptically spotless hospital-waiting-room set — all glass, metal, linoleum, fake plants, and towering walls of Pepto-Bismol-colored tiles. . . .”Work on the project began about a year before the play opened in February (it has been extended through Sunday). Ms. Sanchez remembered the initial meeting with the playwright and director as a general and open-ended conversation about the story and its many big concepts. “The funny thing is the first images that came to mind were of a very floaty kind of world made out of fabrics in reference to the tents of the war, and then I went home and it ended up being kind of the opposite,” she said.The opposite, in this case, being walls, but as abstract forms. “I don’t go much for a naturalistic style,” she said. “I like the three-dimensionality of a space. I like to go into the walls, not be confined by them.” An often overlooked craft, stage design is required to make sense of all aspects of theater: the needs of the written work, the performance space, lighting and sound design, the actors, the director, and the audience, ultimately creating a physical and imaginative space for both actors and audience to inhabit. Given such a monumental task, one imagines that set designers must be a self-effacing lot, happy to lurk in the backstage rather than attempt to hog the limelight. That just about sums up Ms. Sanchez, who seems perfectly content with her life, complete with love, creativity, and ease.One of six sisters who grew up in Mexico City, Ms. Sanchez first worked in architecture. In 1998 she enrolled in the National Autonomous University of Mexico, a highly regarded public university in the capital city with a UNESCO World Heritage Site campus designed by some of Mexico’s best-known modern architects. To her dismay, a yearlong strike shut down the university, so she continued pursuing her architectural degree in a private college, which she didn’t care for, and then at a polytechnic school in Spain.She returned to Mexico City in 2001, after the public university had reopened, and was introduced to set design in one of her classes.“But set design was not an option for me,” she explained recently in alluring Spanish-inflected English while seated at her kitchen table. The world of set designing in Mexico, she discovered, was so tightly controlled by unions that it held little appeal.Instead, she continued to pursue architecture and found work easily during Mexico City’s urban renewal boom in the early part of this century. She took part in the renovation of her father’s 1920s building in the capital, in which the family lived. Soon, her American husband-to-be, who worked in corporate investigations and had been transferred to Mexico City, rented an apartment below theirs.The couple married in 2010 and moved to New York for her husband’s job, which he lost soon after relocating. Unemployed, they began volunteering as theater ushers at small, Off Broadway shows. It was then that Ms. Sanchez decided to apply to the Yale Drama School, where she studied set design and received her master’s degree. She gave birth to her daughter, Galia, while there.At Yale, Ms. Sanchez met Ms. Blain-Cruz, the director of “Marys Seacole.” The two worked together on a notable 2014 Yale Repertory Theater production of “War,” written by Branden Jacobs-Jenkins. It was also the first time the young set designer became aware of being categorized as “colored,” and of racial issues in general, she said. Today, she understands that she is typecast as a Latina set designer and is called to work on plays directed by people of color or those dealing with immigrant experiences.“I know I’m a woman-of-color designer,” she said. “And I’m happy doing what I do.” Her theater credits include various Off Broadway shows at theaters like the Public and Cherry Lane, as well as regional ones in New Jersey, Baltimore, Dallas, Connecticut, and Oregon.Since moving to the South Fork in 2017, she has become increasingly aware of the immigrant community and feels a strong connection to the Latino population here. “Everyone I’ve met here has been so warm. Even though I haven’t had the experience of coming here illegally or having to deal with these issues, there’s no resentment towards me at all. It’s the opposite.”In May, Ms. Sanchez will head west for her third season with the Oregon Shakespeare Festival, where she’ll tackle “All’s Well That Ends Well.” Her husband and daughter will visit during her monthlong stay away from home. “I have to choose my work more cleverly now,” she said about balancing motherhood and work. “Instead of doing eight plays a year, I’ll do four really good ones.”A plan that she hopes will also afford her enough downtime to pursue her other creative passions: painting, ceramics, and making leather bags from scratch.