A day of surprise successes in its financial struggles put a decidedly joyous glow on the National Symphony Orchestra's opening last night. By late yesterday, the symphony was $530,000 closer to solving its $5 million projected shortfall.

Only hours before conductor Rafael Fru hbeck de Burgos heralded the first note of the symphony's 52nd season, a Washington construction firm loaned $500,000, interest free, to the orchestra. Later, at a party at the Kennedy Center, the Arco Foundation quietly presented a $30,000 check. "This is a major grant to keep us playing happily," said Leonard Silverstein, the orchestra's president, of the loan from Blake Construction Co. "They called about 6 o'clock."

Silverstein's smiles were matched by the enthusiasm of Anna Arrington, the program officer for arts and humanities for Arco, the Los Angeles-based oil company. "It's really fun to be here to do this. Usually I can only say, 'We will go ahead and recommend,' but I don't get a chance to hand over the check," said Arrington, who was in Washington to attend a National Endowment for the Arts panel. "We feel the National Symphony is a national organization and national corporations should support it."

Standing at her side, Silverstein couldn't have agreed more. "Our problem is we shouldn't be on a hand-to-mouth existence. We have developed a great product and now that we have that product, we have to play catch-up."

The symphony's growing excellence also added a buoyant confidence to the evening. "It's incredible," said conductor Fru hbeck. "It's the only orchestra in the world that I know of that has steadily improved each season."

The symphony's opening night traditionally signals the start of the social season for Washington's cultural community. Among the guests at last night's black-tie performance and reception were Kennedy Center Chairman Roger Stevens, impresario Patrick Hayes, foundation head and symphony vice president Henry Strong and D.C. Commission on the Arts executive director Mildred Bautista.

Making his own social debut was Spanish Ambassador Nuno Aguirre de Carcer. Since he presented his credentials to President Reagan last Friday, the ambassador has been meeting with State Department officials on international matters including the crisis in Lebanon. "It's a horror and prompts much grief," he said. "It has been a very good decision to send in Marines to help stabilize Lebanon so they can move ahead on their own."

Although the reception had none of the visible trappings of a board meeting, clusters of the orchestra's supporters spent their time busily planning the next fund-raising steps. "We all have been working our tails off, trying to develop new funding sources and holding on to our traditional supporters," said Henry Strong. "The financial situation is serious."