Eight countries -- the three organizing nations and five countries that failed to win a single medal in the 1976 Summer Olympics -- showed up here today for a hastily arranged two-day conference on organizing alternative games to the 1980 Moscow Summer Olympics.

Despite the scant turnout, the conference's organizers, the United States, British and Australia, were optimistic that worldwide support would grow for the campaign to provide other arenas for athletes who boycott Moscow to protest the Soviet invasion of Afghanistan.

President Carter, according to U.S. delegation chairman Lloyd Cutler, "is well aware of the attendance here and he is not at all unhappy."

Cutler, who is White House special counsel, privately predicted that all the major noncommunist Olympic powers except for Mexico will wind up boycotting the Moscow games.

Minister of State Douglas Hurd, head of the British delegation, attempted to explain the low turnout by noting that "there are governments which are determined to boycott, but are not interested in alternative competition. We respect that."

Besides the three organizing countries, the active participants in today's talks were Kenya, Sudan, the Netherlands, Saudi Arabia and the Dominican Republic.

Four other countries -- Canada, Portugal, the Philippines and Costa Rica -- sent observers.

Among the more notable absentees were West Germany, which turned down an invitation, and France, which has resisted an organized boycott.

Cutler and Hurd told a press conference that their idea is to organize a series of events around the world and link them by television satellite so that athletes could get, in Cutler's phrase, "the kind of world recognition that goes with being in the Olympics." He said that such a world television hookup "could be self-financing, and then some" if properly organized.

Among the cities apparently being considered are Brisbane, Australia; Nairobi, Kenya; Montreal and some U.S. cities that reportedly have expressed interest. But the participants in today's conference said they doubted that they would make a list public.

The International Amateur Athletics Federation has said it would bar from any subsequent federation-sanctioned meets any athletes who participate in competitions held at the same time as the Moscow Olympics. Hurd, however, told reporters that the alternative games would probably be held after the Olympics and there was no question of timing them to complete directly with Moscow.

He said the idea was to "build up" the traditional games in many sports that follow the Olympics. The alternate games, he said, would "probably be later, but not much later."

He said the proposed games would be open even to countries that took part in the Moscow Olympics, "probably" also including the Soviets.

"We all accept," said Hurd "that governments don't organize games." He said the conference participants were only trying to map out suggestions. If national athletic organizations "don't find them helpful, that's that," he said.

Hurd seemed to indicate that the decision to hold the conference despite the obvious lack of preparation was made out of concern that a start had to be made immediately if there is to be a serious possibility of organizing the alternative games in time.

There also seemed to be an unstated desire to place pressure on countries that have not yet fully committed themselves to punishing the Soviets. Cutler said, for example, that while Japan has stated its opposition to taking part in the Moscow Games it has not taken the next step of offering the elaborate sports facilities of Tokyo for alternate events.

There are also countries, exemplified by France, who have indicated unwillingness to take part in primarily Soviet Bloc games but have been resisting an organized boycott, They will stay away from Moscow only if it becomes clear that most of the noncommunist world will not be there.

The U.S. mission in Geneva did not learn until this morning that Cutler would be the American representative at the meeting apparently organized on the spur of the moment late last week. Cutler said that the choice of Geneva was made just a few days ago.

Hurd, who chaired today's session at the British mission here, insisted that the conference had been "suggested by osmosis" rather than by his own government. British Prime Minister Margaret Thatcher has been in the forefront of the calls for a boycott of the Moscow Games.

He indicated, however, that Britain would reconsider its stand if the Soviets were to withdraw completely from Afghanistan. "That would be an entirely new situation," he said.

Cutler said that Carter's decision that the United States should boycott the Olympics is final. There are people, he said, who "may still be hoping the president will change his decision. He will not."

Cutler is to chair the second session of the conference on Tuesday at the U.S. mission here.