THE STUNNING swiftness with which Anwar Sadat solicited and immediately accepted an invitation to go to Israel last week masks the careful thought and preparations the Egyptian leader put into his historic action.

Sadat appears to have made his decision to cut through three decades of Arab-Israeli hatred and bloodshed to deal with the Israelis face to face on their own ground both for strategic and tactical reasons. On all levels, things never will be the same again in the Middle East.

He and Israeli Prime Minister Menahem Begin now have established a new negotiating track that runs parallel to the Carter administration's plan for reconvening the Geneva peace conference. But that track is, in effect, independent of American control and free from the veto power of Sadat's Syrian and Palestinian allies.

There are clear signs that the Israelis and Egyptians; perceiving that movement toward Geneva had stalled, set up their own "back channel" diplomatic operation that cleared the way for last week's public rush toward a Sadat appearance in Jerusalem. The key figure in the secret groundbreaking appears to have been Israelu Foreign Minister Moshe Dayan, who has long sought to engineer the kind of mano mano debate Sadat now has accepted.

A still mysterious but now confirmed meeting in Europe between Dayan and an Arab envoy two months ago appears to have pointed the way toward last's week symbolic breakthrough.Other elements of the still developing saga of how the breakthrough occurred include official trips by Begin and Sadat to Romania. Israel's long-standing communication links to Jordan's King Hussein and a sudden hardening of position by Syria that helped convince Sadat to launch a dramatic new initiative to get the Middle East out of an increasingly dangerous stalemate. Sadat's Options.

SADAT HAS made it clear tht he still prefers to go to Geneva with the Syrians and Palestinians at his side, and that he is opening the dialogue in order to present his case rather than cut a deal immediately. But his decision to go to Jerusalem also makes it clear to the other Arabs that Geneva is not his only option.

Sadat's sprint to propose, accept and carry out in less than a week a trip that every other Arab leader has refused even to think about for the past 29 years is designed to reduce the grave political and security risks he is taking. The Syrians, Palestinians, Iraqis and Libyans will have had minimum time to get their propaganda machines in high gear before Sadat is back at home.

Two Arab countries are making no move to crank up serious attacks on Sadat, and they may ultimately ne more important than the hostile barrage he does face. They are Saudi Arabia and Jordan. It is likely that they were involved in the covert, precise diplomatic calibrations that led up to Sadat's surprise moves. The tepid, pro forma criticism the Saudis issued Friday and Jordan's silence suggest that they are at least objective allies of Sadat in his effort to break the Middle East stalemate at enormous risk to his place in Arab history.

Sadat has said that consulted no one about his daring move. But to keep the plan away from Saudi Arabia's ruling royal familY - Egypt's principal Arab diplomatic partner and source of funds since Sadat came to power - would be a complete break with his past practices.

He has checked with the Saudis on even domestic measures before putting them into effect. On a trip that has been kept secret until now, Sadat flew to Saudi Arabia last January in the midst of serious rioting in Cairo to ask the Saudis about his restoring food price subsidies to reduce popular unrest.

It is clear, however, that Sadat did hold his plans from the American policymakers who were formally in charge of getting Geneva going again. State Department aides were working on position papers on Geneva even as Walter Cronkite flickered on the screen and included Sadat and Begin to exchange their epochal offers to meet.

Surprised American officials concede that the Egyptians and Israelis have opened up an independent diplomatic track. They strongly argue, however, that the new track supports rather than undercuts their efforts on Geneva and that the new movement was made possible by the Carter administration's early stress on a comprehensive MIddle East agreement.

But Sadat and Begin have at least temporarily shrunk the Middle East conflict to a regional scale by putting both superpowers at the margins of their action. If Washington was outflanked by the shrewd Egyptian president and the canny Israeli prime minister, Moscow has been totally embarrassed by this brutal demonstration of Russian impotence in the Middle East.

Begin's government has been in open conflict with the Carter administration over the Palestinian question for months and has sought in a number of ways to establish its military and diplomatic independence from Washington. The invitation to Sadat fits those desires as well as Israel's historic insistence that there can be no true peace in the Middle East until the Arabs demonstrate they are prepared to accept Israelis as legitimate residents of the region.

Sadat's motivation in scaling down the central American role that he and Henry A. Kissinger created after the 1973 Arab-Israeli war remains much more obscure. Sadat continues to hold those cards close to his chest as he evaluates Arab reaction. Moreover, the speed and impact of his actions add to a surface impression of impulsive, hasty decisions.

Begin's Victory.

BENEATH THE surface turmoil, however, lies a chain of events and perceptions that stretches back at least to August, according to accounts provided in public by Sadat and in private by diplomatic sources here.Key points on the trail to Jerusalem appear to be Sadat's strong apprehension over Syria's intentions, and his distinct unease with the Carter file inherited from Kissinger.

Many of the essential details of what led to the dramatic exchange between Sadat and Begin remain hidden deep in the shadows of secret diplomacy. Only a tentative outline can be drawn from the events and reports of the past six months.

The first major catalyst is clear, however. It was the upset victory last May by Begin's Likud coalition over the Labor Party group that had ruled Israel for 29 years. In Begin, one Arab ambassador in Paris observed a few months after the election, "we have to deal with a man far more prepared either to make war on us or make a peace with us than were his predecessors. He will make decisions."

In August, after Secretary of State Cyrus Vance toured the region and was unable to deliver Israeli acceptance for Sadat's proposal for a U.S. sponsored "working group" to precede Geneva talks, Sadat went back to the drawing board. While the Islamic world celebrated the holy month of Ramadan, Sadat turned the daily affairs of government over to subordinates and withdrew for a month of contemplation.

He told newsmen in Damascus Thursday that the idea of actually going to Israel to put his case to the Knesset began to take shape during the retreat. Other responsible sources suggest that Sadat actually came back to work with a detailed plan for secret contacts with the Israelis that he put into effect almost immediately.

It was not only Vance's failure to move the Israelis in any way that disturbed Sadat. Geneva was being resurrected as little more than a last resort, and the chances of securing the kind of peace agreement that sadat believes is vital to halting the alarming economic and political deterioration of Egypt were darkened measurably by signals out of Damascus.

Those signals, also picked up in Washington, indicated that Syria was edging its long and bitter feud with neighboring Iraq. An Iraqi-Syrian alliance would have left Syrian ruler Hafez Assad in a position to sit outside Geneva and hammer Sadat in Arab public opinion. Sadat appears to have decided to strike first and far more boldly than the Syrians anticipated.

Sadat and Jordan's King Hussein had become deeply concerned that Syria's rigid stand would abort the peace conference and produce a failure that would lead quickly to another Middle East war - one in which Arab armies would be completed destroyed by the much better equipped and maintained Israeli forces, now reportedly backed by nuclear weapons.

Sadat's highly conciliatory move toward the Israelis comes just as Israel is seeking American approval for what amounts to a new generation of technology and arms superiority that will stretch its current conventional military advantage over the Arabs to the end of the 1980s. Whether by design or not, Sadat's trip tends to bolster those in the Carter administration who are arguing that Israel does not need an enormous new influx of weapons.

Dayan's Travels.

BUT THE ISRAELIS were writing a peace scenario as well as the more frightening war contingency plan. Begin was probably not the initiator of this, however. It was Foreign Minister Dayan, who prides himself on his ability to speak Arabic and deal with Arabs in the flesh. He reportedly sent out word to Sadat through channels he has established to Hussein that a dramatic gesture by the Arabs to get the peace process moving again would not go unrewarded.

Dayan flew to Paris in mid-September, broke off his scheduled continuing flight to the United States and returned urgently to Israel. When he resumed the trip and came to Washington, he gave high administration officials a detailed account of a secret meeting he had held in Paris with an Arab envoy representing Sadat.

The identity of the Arab envoy and the details of the discussion continue to be tightly held secrets. One published account has identified the envoy as a Saudi Arabian officials. By using a Saudi as his intermediary, Sadat would have been assuring Riyadh's approval for any move he took. Moreover, there are a handful of Saudi officials in whom Sadat places absolute trust.

Diplomatic analysts feel that it is highly improbable that Sadat and Begin were operating in an information vacuum last week when they appeared on CBS-TV."Begin would not have extended an invitation if he had not known Sadat was going to accept it," one said flatly.

Sources in Israel have suggested to newsmen that Romanian officials may have played the key go-between role, since Begin and Sadat both have visited that country in recent months. The Israeli leaks, which Sadat has discounted publicly, underscore that the United States had nothing to do with arranging the exchange.

The surprise in the upper levels of the Carter administration has been general enough to rule out any American role, unless it was conducted through the kind of highly covert "back channel" effort that Kissinger delighted in using. He frequently turned to non-State Department channels, especially the Central Intelligence Agency, to conceal even the existence of negotiations from everyone except himself and his negotiating partner. It is plausible to assume that Sadat and Begin would have trusted only a security outfit like the CIA with information on contacts.

The implications of Sadat's decision being a well considered and intricately prepared one rather than a spur-of-the-moment affair are far-reaching. More concretely than he or any other Arab leader has previously done, Sadat has now shown that he is prepared to live in peace with Israel and that he will not give anyone else an absolute veto over Egypt's chances for a peace agreement. He decided last week to go to Jerusalem to put the Palestinian and the Syrian cases, as well as Egypt's, to the Knesset. But he was also setting out to demonstrate that the Egyptian-Israeli talks if nothing else works.

Sadat staked his political, and even his physical, existence on this audacious gamble. Perhaps the most important immediate consequence of this gamble will come, not in Jerusalem but in Cairo, as the world watches to see if its, oldest nation-state follows its most daring statesman