Soon after arriving in Beirut, they learned that their house had been destroyed in the bombing. “At that point, I lost hope to go home,” Abdulrazak said.

The family consulted with officials at the United States Embassy in Amman, Jordan, and with officials of several European Union nations, but they were given no hope that they would all be able to get visas.

Coincidentally, the family had been planning to take a vacation in Cuba and had already been issued tourist visas. So they decided to try their luck there. “It was a gamble,” Abdulrazak said, “but it was better than Syria and Lebanon.”

They flew to Havana in September 2012, and the family applied for refugee status through an office of the United Nations, Abdulrazak said. While they waited for the outcome of their petition, the children attended Spanish classes at a private school for foreigners; the United Nations paid the rent for the apartment where they stayed, he said.

They were approved for admission to the United States in October and flew to Miami on Nov. 19. The following day they flew into Newark, where they were met by relatives, who took them to their new home in Paterson, which has one of the largest Arab populations in the United States. (There are some 175,000 people of Syrian descent living in the United States, according to the Census Bureau, with about 28,000 living in the New York metropolitan area.)

“When you lose your house and your business,” Abdulrazak said, “you have to be courageous.”

The United Nations has set a goal of temporarily or permanently resettling at least 30,000 Syrians by the end of this year. At least 20 countries have pledged a total of at least 18,300 spaces.

The United States, which has already provided about $1.3 billion in humanitarian assistance to the Syrian people, has resettled at least 87 Syrians since fiscal year 2012, State Department officials said. The paperwork for a vast majority of those cases, however, had begun before the onset of the conflict.