A Taco Bell in Times Square aims to ease the burden on employees by having customers order either online or through electronic kiosks in the restaurant, cutting out the traditional cashier-as-middleman experience.

The store is a Taco Bell Cantina, part of the company’s more upscale, open-kitchen chain, and it has been open since mid-April. Customers who order online pick up their food from locked cubbies they can access through a separate entrance, without going into the main restaurant. The cubbies keep the food warm and sound an alarm if it has been sitting too long.

People who place their orders through the 10 digital kiosks at the restaurant entrance grab their food from a designated area in the back.

The location has 70 employees and four production lines to handle the volume of orders from visitors to Times Square, compared with about 35 employees and two production lines for a regular Taco Bell.

The concept predates the coronavirus pandemic—it took about two years to develop—but it chimes with new consumer expectations for a quicker experience with less human interaction and less time indoors, industry experts say.

“It is about that speed, convenience, ease—creating that seamless experience for consumers,” said Noam Dorros, director analyst at Gartner Inc., a research firm.

The Times Square store is Taco Bell’s first location in the U.S. to emphasize digital ordering in this way. The experience of taking food from a locked box is reminiscent of self-service automats, which were ubiquitous in New York for decades before falling out of use. The new store still has an employee at the front counter to make sure customers are old enough to drink alcohol, a fixture of many Taco Bell Cantinas.

Taco Bell opened a similar store in London last year, though without the cubbies and with fewer kiosks.

Moving away from the traditional cash-register experience is one of the many tactics restaurants are trying to attract staff in a tough labor market as customers get back to eating out again amid loosening Covid-19 restrictions, said Nabeel Alamgir, chief executive and co-founder of Lunchbox Technologies Inc., a startup that specializes in building online ordering systems.

Restaurants are experimenting with QR codes, creating cook-at-home meal kits and reaching customers via apps, kiosks and third-party delivery services. Fast-food companies including Chipotle Mexican Grill Inc. and Del Taco Restaurants Inc. are testing drive-through locations for picking up online orders and Taco Bell’s parent company, Yum Brands Inc., recently acquired a startup to help it start taking orders via text.

“What we’ve done in Times Square is not the finish line for us,” said Mike Grams, Taco Bell’s global chief operating officer. “It is going to take more time…and this constant evolution in innovation around the restaurant experience, which is just becoming so important.”

Taco Bell’s cubby system comes in the wake of similar concepts tried by other chains, both successes and failures. Companies including Sweetgreen Inc. and Cava Group Inc. have dedicated areas for customers to pick up their food.

Eatsa, a restaurant chain that served up quinoa-based meals, tried a digital-only, cubby-pickup model but closed its handful of locations and since 2019 has been providing technology for other eateries under the name Brightloom.

New consumer experiences still require employees to guide, support and provide assurance to customers if something goes wrong, experts said. Many consumers got used to new digital experiences, like buying online and picking up in store, during the pandemic, but companies still have more work to do.

“We have to start engaging with customers in ways that respect their real lives,” said Jeannie Walters, chief executive of Experience Investigators, a customer-experience consulting firm.

Write to Ann-Marie Alcántara at ann-marie.alcantara@wsj.com

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