The thing is, Mr. Rivera never had any intention of selling meat.

A New York City native and barbecue aficionado, he became obsessed with a piquant sauce he tasted in 2009 at a Mets game. He set out to recreate it at home, a quest that led him to quit a secure job as an executive chef and enter culinary school.

By 2019, he was marketing his own sauces, which evoke flavors of traditional Puerto Rican cooking. He used the Father & Son’s moniker, with a label featuring a snapshot of him and his son stirring a pot.

Then the pandemic and an injury kept him home. Mr. Rivera trawled online for insights.

In 2021, he started selling his sauces on the weekends at the Gun Hill Brewery in the Allerton neighborhood of the Bronx until it closed last month. A friend brought a smoker for meat to make it easier for customers to taste sauce samples. Food ran out in three hours, he said.

“The food outshone the sauce,” he said. “The breadwinner was the food.”

What Mr. Rivera assumed would be a weekend one-off is now on the verge of becoming something else, he said: a full-time small business, with help from his wife, Jasity Soltero, their 17-year-old son Mason, and some cousins as needed. Mr. Rivera has developed a menu featuring his take on Puerto Rican classics like roast pork or yellow rice with pigeon peas. He wants to remind people that Puerto Rico’s Indigenous people also barbecued meats.

“He has the best-tasting brisket I ever had,” said Miguel Antonio Salamanca, a chef, at a recent community festival at Co-op City. He added: “I felt this was the place to be.”