A makeshift fleet of more than 150 American yachts, freighters and fishing boats has arrived from Florida in the past 24 hours to pick up the many thousands of Cubans who want to leave this country behind.

By all appearances, they are the first wave of a massive, do-it-yourself shuttle devised by U.S.-based Cuban exiles ferrying their friends, relatives and other refugees from the communist to the capitalist world.

All day, this irregular fleet could be seen hugging the coastline, laying a white trail past Havana as they chugged on to their port of call, Mariel Bay 20 miles to the west.

Sometimes no larger than a large rowboat, these vessels are a symbol of President Fidel Castro's mockery of international diplomacy. The United States and other nations willing to accept refugees has prepared an orderly airlift and a processing center in Costa Rica to bring out and distribute more than 10,000 anti-Castroites who jammed into the Peruvian Embassy three weeks ago.

But Castro, forcing the U.S. hand, gave the green light earlier this week to the Cuban exiles in Florida to come and pick up the refugees now, with no delays or detours.

Now that the lid is off, Cubans for and against Castro seem to talk of little else. Officials said Cuba is being inundated with telephone calls from people in the United States telling friends and relatives to go Mariel and wait to be picked up.

The state telephone and the Western Union cable offices in downtown Havana were beleaguered by people scrambling to send word to the United States.

Outside the telephone exchange, a sign went up saying that only 200 calls could be made from public booths, starting at 7 A.M. and that preference must be given to people with private telephones.

A steady stream of taxis and cars crowded the coastal road to the port of Mariel. Police roadblocks were set up to check travelers' identy cards along the 40-minute drive.

The Cuban authorities clearly want to avoid a wild invasion in Mariel. Anticipating a strong response to the invitation that Cuban exiles come and get refugees, the government two days ago brought in reinforcements of Army, Navy, police and Red Cross workers.

The exit operation here is still very low-key. The small town itself looked deserted. Out of sight of the towns-people, refugees climbed on board of the craft. Some dangerously small pleasure boats had people clinging to the cabins.

In the docking area, the military turned away people without exit documents, telling them to go to Havana to get permits and passports. Last night, eyewitnesses said, the area was strongly lit to avoid people sneaking on board boats.

The procedures for arriving ships are roughly as follow: a boat captain gives the names for friends and relatives he has come to get and he is told that he should also take some refugees who had been in the Peruvian Embassy.

The officials reportedly then promise to locate the friends and relatives, take them to the emigration headquarters and bring them by bus to Mariel.

In Havana, many people who had been refugees in the Peruvian Embassy anxiously waited for the knock on the door. Not all went smoothly. In one family, the father and two sons had been given their passports but the mother's had been withheld without explanation. Desperate, the woman said she had not been able to sleep all week.

Another couple were given exit papers for only one of their two small children. The only explanation they would accept was that this was a form of punishment.

Although the state-controlled media has often announced that Cubans must show "discipline and maturity" to people leaving, there are still frequent reports of harassment. Today's crowd outside the telephone company was attacked by hecklers throwing tomatoes and eggs and shouting "You garbage" or "You parasites."

Several families who had been inside the Peruvian Embassy for six days said they had been too terrified to leave their houses once they left the compound. They described being constantly hassled by their local block committees. One man said he was told he had better not show up for work because he would "be beaten to death" and the children were no longer allowed in school.

With no income and their ration books confiscated, they said, they depended on relatives to give them food. One couple said their refugee neighbors had been beaten by block committees who had broken into their home at night. Yet many other families report they had no problems.

The Cuban Foreign Ministry, in a statement today, definitely ruled out reestablishing the airlift from Havana to Costa Rica. Only people who had been allotted a place to settle in Costa Rica would be allowed to travel there, but Cuba would not permit anyone to settle in a temporary camp, the statement said.

Earlier this week, Costa Rican President Rodrigo Carazo had called Castro's bluff, saying he would take all the 10,000 Cuban refugees who had entered the embassy. But today's statement seemed to respond to this, saying, "We know that the great majority want to live in the United States or other countries."

A Costa Rican Airlines jet arrived unexpectedly in San Jose, Costa Rica, tonight, carrying 107 Cuban refugees from Havana, the Associated Press reported.

[Government officials did not explain why the plane had been allowed to leave Cuba or if the government in Havana had agreed to allow other refugee flights to Costa Rica, the AP report said.]