Mr. Heredia is one of about 25,000 Cubans who arrived by land and sea in the United States without travel visas in the fiscal year that ended on Sept. 30, according to government figures. He, like many others, is also an unexpected throwback to a time that experts thought had long passed: the era when Cubans boarded homemade vessels built from old car parts and inner tubes, hoping for calm seas and favorable winds. As the number of Cubans attempting the voyage nearly doubled in the past two years, the number of vessels unfit for the dangerous 90-mile crossing also climbed.

Not since the rafter crisis of 1994 has the United States received so many Cuban migrants. The increase highlights the consequences of a United States immigration policy that gives preferential treatment to Cubans and recent reforms on the island that loosened travel restrictions, and it puts a harsh spotlight on the growing frustration of a post-Fidel Castro Cuba.

More Cubans took to the sea last year than in any year since 2008, when Raúl Castro officially took power and the nation hummed with anticipation. Some experts fear that the recent spike in migration could be a harbinger of a mass exodus, and they caution that the unseaworthy vessels have already left a trail of deaths.

“I believe there is a silent massive exodus,” said Ramón Saúl Sánchez, an exile leader in Miami who has helped families of those who died at sea. “We are back to those times, like in 1994, when people built little floating devices and took to the ocean, whether they had relatives here or not.”

Although the number migrating by sea hardly compares with the summer of 1994, Mr. Sánchez said the number of illegal and legal Cuban immigrants combined has now surpassed the number of those who arrived during the crisis 20 years ago.