The United States and China formally crossed a three-decade-old diplomatic gulf today with an explosion of firecrackers and toasts in California champagne.

Vice Premier Teng Hsiao-ping joined dozens of other Chinese officials at the American liaison office here to celebrate the first day of full U.S.-China relations since 1949.

In his toast, Teng complimented President Carter, whom the Chinese leader will meet in Washington soon, for his "far-sighted view" in ending ties with the Nationalist Chinese on Taiwan and recognizing Peking as the real capital of China.

"I feel certain that the far-reaching influence the establishment of diplomatic relations between our two countries exerts... upon the defense of world peace will become more and more evident with the passage of time," Teng said.

Teng, accompanied by Foreign Minister Huang Hua, was the highest-ranking Chinese official by far to set foot in the building that has been the U.S. headquarters here since American diplomats arrived in 1973. The full relations baginning today are expected to ease American access to important trade and industrial departments of the Chinese government and speed a hoped-for trade bonanza for the two countries.

"Through our mutual efforts," said Leonard Woodcock, the liaison office chief, in his toast, "we are now able to concentrate our energies on building the more permement and effective institutions that full diplomatic relations make possible."

The guest list of about 100 Chinese who arrived with smiles and congratulations was headed by leading figures in science and industry, an indication of the key areas of exchange between the world's richest nation and the world's most populous nation.

They included Fang Yi, the politiburo member responsible for science; Foreign Trade Minister Li Chiang, Chemical Industry Minister Sun Ching-wen, National Airline Director Shen Tu, Vice Petroleum Minister Chang Wen-ping and leading scientists Chien San-chiang and Chou Peiyuan.

The American diplomats here were joined by a visiting House Banking Committee delegation led by Rep. Thomas L. Ashley (D-Ohio). The delegation and Chinese officials have discussed the prospects for the release of Chinese assets frozen in U.S. banks since 1950 which are blicking direct American banking relations with Peking. Committee staff said they are also preparing legislation to make China eligible for U.S. Export-Import Bank loans.

Rep. John J. LaFalce (D-N.Y.) decorated Teng with an American and Chinese flag pin. Outside, firecrackers. carefully laid out by theliaison office's Chinese staff punctuated the toasts. Guests inside sipped champagne, Coca Cola or Chinese orange pop and munched snacks, including egg rolls and slices of apple pie.

Teng, at 74 the most experienced and influential leader in the Chinese government today, seemed tired and moved slowly.

At one point he caught the heel of one of his shoes on the edge of a rug and could not extricate himself until an aide lifted the vice premier's leg and set it down on the rug.

Teng has just climaxed a year of extraordinary activity, including a decision to normalize relations with the United States and the announcement by the full Communist Party Central Committee that the nation would end mass political campaigns to devote all spare moments to economic modernization.

The decisions reflect Teng's determination to put aside dogmas of the late Mao Tse-tung if they interfere with raising individual standards of living and strengthening national defense.

The small and generally young American contingent here crowded around to take snapshots of Teng and discuss the growth that is to come when the building becomes an official embassy March 1.

Today's gathering inaugurated a new era of good felling in Sino-American relations, which have been rising and falling for centuries. American traders throughout the 19th century dreamed of lucrative trade with China's millions, but they never seemed to realize their expectations as the last of China's dynasties fell and political chaos ensued.

American missionaries and politicians applauded experiments in democracy early in this century, but U.S. diplomats grew disheartened as the new National Chinese government gave way to corruption and devoted more effort to fighting Chinese Communists than to repelling the invading Japanese.

A brief opportunity in 1949 to open full relations with the nation's new Communist leaders collapsed bacause of rising anti-communism in the United States.Then came the Korean War.

In the late 1960s, however, President Johnson beganto ease travel restrictions with China. In 1972 President Nixon visited Peking and laid down the formula of U.S. withdrawal from Taiwan that finally brought normalization under President Carter.