Beyond the theatrical surprises that President Anwar Sadat has sprung upon an unprepared world in the past month, Egypt still believes that the United States will play crucial role if a negotiated peace settlement is to be achieved in the Middle East.

In fact, it is becoming clear on the eve of Secretary of State Cyrus Vance's tour of the region that much of what Sadat has done has been aimed at influencing American opinion and, the Egyptians believe, helping President Carter do what he wanted to do but did not know how.

By his action today in ordering the Soviet Union and some East European countries to reduce their consular and cultural missions in Egypt, Sadat has virtually cut himself off from Egypt's former ally, Moscow.

But his hopes for U.S. assistance in the peace negotiations are not a result of his break with the Soviets. He wants an active American role because he believes that only the United States can prod Israel into giving him acceptable terms for a settlement.

Carter's statements of support for Sadat in his Nov. 30 press conference and more importantR, this week's news that Vance was coming out to the Middle East to give Sadat wht help he can, ended a period of some anxiety and tension here over how Washington would respond.

Two weeks ago, Egypt's acting foreign minister, Butros Gahli, was asked if it was still true, as Sadat has so often said in the past, that "the U.S. holds 99 per cent of the cards in the Middle East."

Boutros Ghali, who was new to his job at the time, replied, "it is time for a change in the proportions. The decisive moves are now up to Israel, Egypt and the Palestinians."

But when he was asked the same question yesterday, the figure was back to 99 per cent - a reflection of his own growing awareness that Sadat considers it essential for the United States to take a strong hand in the forthcoming negotiations.

Sadat has said as much in the many interviews he has given since his return from Jerusalem, but the headline-making events that have thrown the Arab world into turmoil have tended to obscure this aspect of his initiative.

Authoritive Egyptian and foreign sources who are in frequent contact with Sadat say that the president had formulated this analysis of the regional negotiating situation.

Carter had the right instincts and in his call for a Palestinian homeland, had shown that he was more understanding of Middle Eastern realities than any previous U.S. leader. But he made mistakes - mistakes that, in Sadat's view, had brought the "peace process" to a standstill.

By allowing the Panama Canal treaties and the energy program to come up in Congress at the same time he was trying to break new ground in the Middle East, Carter weakened himself and strengthened the hand of the Israeli lobby, the Egyptians believe.

By failing to develop a strategy for selling his ideas on peace to the American supporters of Israel, Carter left himself vulnerable to their anger when he took steps they disapproved of such as issuing the Soviet - U.S. working paper. He then backed down from this under pressure from the Israeli lobby, the Egyptians say.

In addition, the Egyptians feel Carter gave Israeli Prime Minister Menahem Begin a "unearned victory" on his trip to the United States last summe, allowing Begin to score a public relations success without gaining any visible movements toward a peaceful settlement.

With Carter thus weakened and with Israel suspicious and mistrustful of both Carter and the Arabs, it became necessary for Sadat to do something that would break the "psychological barriers" erected by 30 years of war, help Carter, and show the Israelis that Egypt was serious about peace.

By going to Jerusalem, Egyptian officials say, Sadat has made it possible for the Israelis to accept American suggestions on steps toward peace without looking as if they are taking orders from Washington.

Sadat's initiative has also eased American domestic pessure on Carter, giving him room to maneuver without having to protect his flanks. The report that prominent American Jewish leaders were criticizing Carter for giving Sadat enough support had an electrifying effect on Egyptian officials, who saw this as a sign that the policy was working.

"Now the pressure for peace is coming from inside Israel, from the U.S." an authoritiative Egyptian official said with satisfaction. "That leaves Carter free to operate indirectly and he can be more effective that way."

The United States was not informed in advance of Sadat's decision to go to Israel or of his call for a preliminary conference in Cairo because, according to sources, the Carter administration had turned down earlier Egyptian proposals for a startling initiative. Sadat did not want to be rebuffed again since in his view, the American insistence on a Geneva conference as the only forum for peace talks was going nowhere.

Egyptians were well aware that U.S. headlines at the time of the Jerusalem trip read "Carter backs Sadat but . . ." They were aware of U.S. concern that Sadat not bolt to a bilateral accord with Israel. Sadat had repeatedly insisted that he would not do that, but the United States has been sending him messages intended to reinforce that determination.

On the morning of Sadat's speech to the Egyptian parliament, in which he issued the call for a preliminary conference in Cairo, U.S. Ambassador Hermann Eilts, on instructions from the state Department, asked him to defer it.

When he went ahead anyway, Washington waited three days before giving the conference what some here saw as a likewarn endorsement.

Egyptian officials say they understand that the proposal was dropped on the United States without much warning - and on Thanksgiving weekend - so some hesitation in Washington was understandable. But at the time, there were officials who wondered whether Carter was not trying to rein in an Egyptian leader whom he viewed as out of control.

Sadat has maintained throughout that he has complete faith in Carter and takes him at his word. "That man is honest, that man is true," he told American TV interviewers.

Members of Sadat's staff say that despite the anxiety that some Egyptians felt when they thought Carter was trying to delay the Cairo conference, they have no reason to believe that his endorsement is anything but genuine now that he has made up his mind.

To the Egyptians it is a matter of more than passing interest. Whether or not Vance is effective in persuading some of Sadat's opponents in the Arab world to moderate their criticism, the Egyptians believe that only the United States can finally prevail on Israel to give up the territories occupied in the 1967 war. Sadat is understood to have come back from Israel saying he found more flexibility there than he had expected, but he is also staying in effect, that he needs the United States to jog them along a bit.