With Israel's return of the last occupied part of the Sinai Peninsula to Egypt, the United States has scored one of the great landmark successes of modern diplomacy. But it leaves this country under immediate and unavoidable pressure to prove that its success is not also the epitaph for the Camp David process that brought it about.

Since its inception at the meeting of American, Israeli and Egyptian leaders in August, 1978, that process has been the fountainhead of U. S. Mideast policy. Now, an increasingly skeptical world will be watching to see whether President Reagan can come up with an encore demonstrating that there is still enough life in the Camp David process to retain it as the principal vehicle for seeking a Mideast peace.

Yesterday's withdrawal of the last Israeli forces from the Sinai after 15 years of occupation brought to a successful conclusion the first of the three goals set forth in the Camp David accords--laying the foundation for a permanent peace between Israel and Egypt.

But the other two objectives remain. They call first for achieving an agreement on self-rule for the Palestinian inhabitants of the Israeli-occupied West Bank and Gaza Strip and, second, for moving forward, with the engagement of the larger Arab world, to a comprehensive settlement of the Arab-Israeli conflict that has kept the region in turmoil for 34 years.

It is in regard to these areas that an increasingly large segment of world opinion has concluded that Camp David is too limited and creaky a vehicle to repeat its initial success. If the United States is to turn back the growing call for new approaches--some of them advocating the introduction of the Palestine Liberation Organization and the Soviet Union--it must quickly and convincingly disprove the idea that the Camp David accords are obsolescent and ready to self-destruct.

Specifically, that means the United States must now give priority attention to trying to achieve the second of the Camp David goals. The Egyptian-Israeli negotiations for an agreement on Palestinian autonomy have dragged on for three years; the Reagan administration, as the willing inheritor of the Camp David process, is keenly aware that it can no longer evade demands for a high-level U. S. involvement aimed at breaking the deadlock and wrapping up a workable agreement.

In fact, the administration's Mideast timetable calls for mounting such a push, probably in June; and U. S. policymakers are deciding what tactics and mechanisms are likely to be most effective. Under discussion are such ideas as adopting former president Carter's approach of naming a special, high-level American mediator to engage in the talks, of having Secretary of State Alexander M. Haig Jr. take on that function, or emulating the original Camp David meeting by bringing Reagan together with Israeli Prime Minister Menachem Begin and Egyptian President Hosni Mubarak.

Administration officials privately acknowledge that they soon will have to choose one of these routes and try to "bulldoze" through to an agreement. The tendency to use the term "bulldoze" is perhaps the clearest sign that these officials are under no illusions about the formidible obstacles they face.

The central problem is whether U. S. mediation can bridge the vast gap between Israel's efforts to sharply limit Palestinian autonomy as a way of preserving the Jewish state's hope of eventually absorbing the occupied territories, and Egypt's insistence that the agreement be a stepping-stone to self-determination and the possible creation of an independent Palestinian state.

Tangled in these differing attitudes is the question of whether a compromise capable of winning endorsement by both governments will be sufficiently agreeable to the Palestinians to entice them away from their loyalty to the PLO and convince them to cooperate in making autonomy work.

In addition, a host of other problems lie scattered across the Middle East like land mines and could explode in ways that might blow the autonomy talks irretrievably off course.

These include lingering Israeli fears that Mubarak, with the Sinai now safely back under the Egyptian flag, might greatly downgrade or even abandon his commitments to Israel in favor of ending Egypt's estrangement with the Arab world. On the other side, there is Egyptian concern that Begin's tough and irrascible style of dealing with adversaries could lead Israel to strike at the PLO or other Arab states in ways that Egypt would be unable to ignore.

Here the chief problem involves Israel's increasing frustration with PLO forces in Lebanon and the threat that cross-border raids and retaliations pose to the fragile cease-fire on the frontier dividing the two countries. The United States was so fearful of Israel using a provocation from the PLO in Lebanon as a pretext for delaying the Sinai withdrawal that it let last week's Israeli air strikes into Lebanon pass with a protest so subdued that it was almost inaudible.

Lebanon remains a tinderbox that could explode at any time into an Israeli-PLO showdown that could not only derail the autonomy talks but also widen into a protracted conflict involving other countries.

Yet another major problem is rooted in questions of whether the administration can balance its "strategic consensus" policy of cultivating close military ties with anti-Soviet Arab countries against Israel's fear that providing sophisticated American weaponry to these nations is tipping the Mideast power balance in favor of the Arabs.

The suspicions and recriminations generated last year by Reagan's decision to sell advanced aircraft equipment to Saudi Arabia was a big factor in setting back the administration's timetable for coming to grips with the autonomy issue, and the problem is certain to arise again.

That is especially the case at a time when Iraq's losing war against Iran threatens to topple the Iraqi regime. Resulting fears of a domino-like radicalism and instability spreading through the oil-producing states of the Persian Gulf have made Washington more determined to shore up the military capabilities of friendly governments in the area.

The next test of the administration's ability to pursue its two-track approach to the Middle East is likely to come over Jordan's desire to acquire new U. S. jet fighters and mobile missiles. Israel is fiercely opposed to such a deal.

These are only the most visible of the obstacles and pitfalls that the United States must circumvent if it is to keep the Camp David process intact and on course toward an autonomy agreement. In the view of many critics, the Reagan administration has made the task even more difficult for itself by putting the peace process on hold for so long.

Initially, the administration delayed because it came into office expecting Begin to be defeated in elections last summer. The U. S. timetable for the Middle East ran into further setbacks because of Begin's comeback in the elections, disputes between Washington and Jerusalem over a number of issues including the Israeli bombing of Iraq and the Saudi aircraft sale, the murder of Egyptian President Anwar Sadat and the initial uncertainty about Mubarak's ability to consolidate his hold as Sadat's successor.

As a result, it wasn't until the beginning of this year that Haig got around to focusing on the autonomy question by making two trips to the Middle East to explore chances for negotiation.

According to U. S. officials, he found that the Israelis, nervous to the point of trauma about the prospect of surrendering the Sinai, and the Egyptians, still calming the unrest stirred by Sadat's assassination, were unwilling to undertake controversial new negotiations at that time. Accordingly, Haig backed off.

The critics, while conceding that much of the delay was unavoidable, still argue that more should have been done sooner. They note that when last-minute problems arose over the Sinai requiring the presence of a top-level U. S. official, Haig was enmeshed in an intercontinental shuttle mission over the Falkland Islands crisis and had to send his deputy, Walter J. Stoessel Jr., to the Middle East.

As one former official who dealt with the Middle East during the Carter administration said last week, "There are always going to be situations like the Falklands. You can't ignore them, but neither can you ignore the Middle East. The problems are still there, and they've been left alone for too long while this administration has given too much attention to areas that are not nearly so crucial to U. S. interests."

The ex-official added: "The Arab world, the Soviets, our allies in Western Europe--all are ready to proclaim that Camp David is dead. If the administration is going to show that it's still alive and breathing, it must start doing so right now. It no longer has the luxury of time."