A happy, enthusiastic crowd turned out along Fifth Avenue and in Central Park yesterday to applaud Israeli Prime Minister Menachem Begin and wish Israel a happy birthday.

Although Begin's hardline positions on returning territory to Arab nations have caused dismay among some American Jews, for many more, the prime minister has become a symbol through whom they express support for Israel.

As Begin addressed thousands standing in the sunshine in Central Park, there was one "Peace Not Territories" sign held aloft.

That anti-begin sign was far out-numbered by placards praising him and even by buttons and T-shirts appearing to espouse the anti-Palestinian position of the militant Jewish Defense League.

Taking Vanessa Redgrave's Oscar-night phrase as a badge of honor, a number proclaimed "I'm a Zionist hoodlum."

In his speech and a television appearance on "Meet the Press" (NBC, WRC), Begin broke no new ground, but ended his week-long visit to the United States on the occasion of Israel's 30th birthday with a fervent declaration that "Israel will never be destroyed."

The theme of the three-hour-long birthday parade up Fifth Avenue was "It's great to be 30 after 4,000 years." and Begin recalled some of the tragedies in history of the Jewish people, including the destruction of Judes 1,908 years ago by Roman legions who declared that it would never rise again.

"Thirty years ago Judea rose again," Begin said.

The New York rally was Begin's final public appearance before flying back to Israel. He began his visit knowing that increasing numbers of American Jews were questioning his policies following Egyptian President Anwar Sadat's trip to Jerusalem last November. Begin told audience after audience that it is vital for American Jews to stand together in support of Israel.

Begin passed up a final opportunity to clarify where his government stands in the face of President Carter's announced determination to link new jet planes for Israel with sales of jets to Saudi Arabia and Egypt.

On "Meet the press," Begin sides-tepped a question on whether Israel would prefer to see all three plane deals go forward or all three canceled it efforts to break the package into three separate parts fail.

He did not mention the planes for Egypt, but stressed that F15s in Saudi Arabia would be dangerous to Israel's security.

In what New York Gov. Hugh Carey reminded the crowd is the second largest Jewish state in the world, New York politicians not surprisingly turned out in force for the birthday. Mayor Edward Koch, Sens, Jacob Jav-its (R) and Daniel Moynihan (D) and a dozen others marched up Fifth Avenue to reviewing stand and took their places with Begin, whom Koch called "a prince of Israel."

The parade featured floats, high school marching bands and participants from many Jewish organizations. Jewish chapters of the New York police department, transit police, and the housing police got warm applause as they marched by.

So did a fire department delegation led by a man with a bullhorn who asked the crowd: "How about a little applause for the nice Jewish firemen."

One organizer said 1 million people watched people at least a part of the birthday celebration organized bu the American Zionist Youth Foundation. Security was tight. The crowd was perhaps a tenth that size, but it jammed the cleared area where Bwgin spoke, and lined the avenue from 54th to 86th Street on a day that began chilly and overcast and ended in warm sunshine.