GoPuff can offer premium virtual shelf space, custom product categories and the opportunity to conduct highly targeted sampling campaigns, which has drawn interest from consumer goods manufacturers that want to reach the millennial market, Gola said.
Indeed, consumer expert Gutfreund said the role of the brand is interesting, as people rely more on delivery services. "Are consumers buying specific brands — supported by advertising and media — or are they buying the delivery service and allowing the delivery companies to select the products for them? Do I buy shampoo or am I buying Suave? Am I buying laundry detergent or Tide?"
Daniel Shpigel, 23, also a former Drexel student, heard about goPuff through word of mouth and is a customer as a medical student at Thomas Jefferson University in Philadelphia.
"Everybody at Jefferson has heard about it now, too," said Shpigel, who likes to order healthy microwave dinners. With frequent exams and a tight schedule, Shpigel said he and his roommates like the convenience of delivery, even though there are stores within walking distance.
While there are many on-demand delivery services in the United States, goPuff is unusual in operating its own warehouses, Ilishayev said, allowing the company to control the user experience from start to finish. The app's predictive algorithm allows the company to keep on top of inventory and know when to restock, reducing the risk of running out at the warehouses and eliminating the need to call customers for a product change.
Another delivery service start-up, Postmates, connects customers to local couriers who deliver anything sold in any store or restaurant in minutes. Postmates has raised more than $138 million in seven rounds of venture capital, according to CrunchBase. It operates in 40 major U.S. cities and states as its plan nothing short of creating the on-demand delivery infrastructure for every major city in the world. Postmates didn't respond to a request for comment about goPuff.
Big tech companies are also aggressively expanding into on-demand delivery — not just Amazon. Alphabet's Google Express plans to cover the entire United States by the end of the year, according to a recent report in Business Insider.
Ilishayev cited two delivery businesses that failed around the turn of this century, including warehouse-based grocery delivery service Webvan — which collapsed after reaching a more than $1 billion market value — as reasons that others may be skittish about warehouses. "One of the most epic fails in the dot-com bubble fiasco," according to CNET.
Those businesses, however, predated the app boom and other significant technology and cultural changes that make on-demand delivery so popular now. "The rise of mobile purchasing, through apps specifically, has certainly opened the door for businesses like ours. Our customers are almost never more than an arm's length from their phone and, by extension, a potential order. Customers can get what they want, when they want it, with no more effort than opening their favorite social media app," Gola said.
— By Dinah Wisenberg Brin, special to CNBC.com