MIAMI (AP) _ The number of Cubans reaching Florida by risking their lives at sea in small boats and rafts hit a record Saturday as people flee their island's political repression and deepening poverty.

No one knows how many die trying to cross the 90-mile Florida Straits between Cuba and the mainland. But those who make it safely find relatives, friends and a social net that swiftly offers them homes, jobs and the one thing they most want - freedom.

''Is good to be here, because I'm free,'' stammered Carlos Alberto Verde, eagerly trying out his few words of English while waiting to be processed at a volunteer refugee resettlement agency here last week.

The previous record number of rafters - excluding the 1980 Mariel boatlift that brought 125,000 Cuban refugees to the United States - was set last year at 2,557. That record fell Saturday, with 2,560 successfully making the trip so far in 1993.

A Coast Guard spokeswoman took the occasion to warn against the hazardous voyage.

''The most important thing we stress is that is a terribly dangerous journey, and the Coast Guard stresses not to do it,'' said Petty Officer Simone Adair in Miami. ''The waters are treacherous. There's no assurance they're going to be located. The sun is brutal, and there are sharks.''

That didn't stop Verde.

Last Monday, 27-year-old Verde piled into a stolen boat after dark with 16 relatives and friends on a quiet beach outside Havana.

They were lucky. They reached the Florida Keys the very next day.

Two days after that, Verde sat beaming with his parents, who earlier settled in Miami.

''I left because I didn't like the (Communist) system,'' said Verde, who was unemployed before leaving Cuba, ''and because of the hunger.''

A few feet away, a member of the Church World Service staff was busy offering new arrivals box lunches, filling in immigration forms, arranging Social Security cards and phoning relatives and friends.

The staff are old hands at resettling Cuban refugees. One is Ernesto Sanchez, a jack-of-all-trades who left Cuba with six friends on a leaky raft just six months ago.

''We were so worried because my country's getting, uh, maybe a civil war, something like that; and the government policy is a very wrong policy, oppressing the people,'' said Sanchez, 29.

''Here I got freedom. I got my job. I got my room, I rent a room. I got my car. I got my friends. I got my freedom. I can live and work without any worry or anything. I don't have to steal anything.''

Sanchez and his friends were picked up at sea by the crew of a freighter, transferred to a Coast Guard cutter and dropped off at Key West.

They were were taken to the Transient Center For Cuban Refugees run by Arturo Cobo, 52, who fled the Castro government 32 years ago.

Along with clothing and medical attention, the center puts new arrivals in touch with families, Cobo said.

''As soon as they arrive here, we spread the news of their arrival to at least 10 radio stations and newspapers and TV. And then, we notify the family of the refugees in Cuba that they are alive and in good health,'' he said.

Word also is passed to Cuban communities in Puerto Rico, New York, New Jersey and Connecticut, he said.

After a day or two, refugees are driven to Miami for further processing by the U.S. Catholic Conference and World Church Service, a support agency run by the National Council of Churches.

''We're working - easy - you know, 12-hour days, seven days a week because people are coming,'' said Roseann Micallef, director of the Church World Service's Immigration and Refugee Program office in Miami. ''There are morning boatloads, and now evening boatloads, and now Saturday and Sunday boatloads, too.''