Saatva has added two other lines of mattresses, foam and latex, and offers three firmness levels. The company had gained enough visibility to be asked to donate a mattress for Pope Francis during his visit to a Philadelphia seminary in 2015.

Saatva’s financing route stands in contrast from its biggest online competitor, Casper. That company went the more typical start-up route, with backing from prominent venture capitalists and even actors, such as Leonardo DiCaprio.

Those who buck the odds by “bootstrapping” their own enterprises are rare, experts say.

“It’s a huge anomaly,” said Mark Walsh, head of innovation and investment at the Small Business Administration. He estimated that as few as one in 50 brick-and-mortar companies and one in 10 online companies could build their businesses into $50 million or $100 million enterprises on their own.

But taking venture capital can be risky. In their haste to get financing, start-up founders often fail to read the fine print and later discover that they have signed away huge shares of the profits. In some cases, founders may be removed by the board of their own companies by the time the businesses are rapidly growing or plan to go public. For these reasons, some founders opt to take debt capital from banks and investors instead of giving away equity.

Spokeo, an online people search engine, has been able to generate tens of millions in sales without venture backing.

“We don’t need it,” said Harrison Tang, a founder of Spokeo. But Mr. Tang, 34, did not always feel that way. When he created Spokeo with three college buddies from Stanford University in 2006, he tried to get equity financing, but was turned down by more than six angel and venture capital investors. Even his father, an entrepreneur himself, told his son he never expected to get the money he lent him back.