AT ONCE, predictably, diverse explanations were offered of the assassination of Anwar Sadat. The shaken government in Cairo insisted that the conspirators were few in number and linked, if at all, to feeble (and fanatical) domestic opposition groups and certainly not to foreign sources. Some of the government's critics countered that the assassination resulted, at least indirectly, from earlier manifestations of unrest in Egypt and from President Sadat's crackdown against elements opposed to his basic line of alliance with the United States and peace with Israel. The new government is not eager to define the threat in terms larger than it feels able to cope with at the moment. Just as obviously, some of the critics have an eye to making political capital of their own.

Who is right? From their own experience with assassinations, Americans should know how difficult it is to establish proof of one or another theory, or even to agree on what the standards of proof ought to be. They should also know how vast are the policy implications of the different possible answers. The real-life difference between an Egyptian version of the single-assassin theory and a full-fledged domestic or international conspiracy theory is conceivably the difference between stability and upheaval at home and between war and peace. Even to speculate quietly about the more far-reaching possibilities is a form of psychological pressure on the new leadership.

If no final explanation of Mr. Sadat's murder can be expected soon, it is, nonetheless, impossible and imprudent not to try to assess what the transfer of power to President-designate Hosni Mubarak may mean. Certain things are self-evident:

Mr. Mubarak must now earn on his own the power he was given by another.

Whatever his inclinations and first steps, he can hardly have the deep personal commitment that Anwar Sadat had to policies that he originated and that he pushed through an often resisting bureaucracy by the force of his own will.

He will be required to prove himself right off by his dealings with opposition elements in Egypt-- those in the streets, the mosques and elsewhere.

He faces a momentous and not unrelated decision in foreign policy: whether, in the absence of more promise than now exists in the Palestinian autonomy talks, to complete normalization of relations with Israel in order to get Israel to evacuate the last third of the Sinai on the Camp David schedule of next April.

He will be the object of an intense Israeli-Saudi tug of war. The Israelis, not without deep misgivings, will likely urge him to stay on President Sadat's evident normalization-evacuation course. The Saudis will beckon him back to the Arab fold, urging him to follow their Palestinian lead.

In brief, notwithstanding the dedication to continuity professed in Cairo, Jerusalem and Washington, it is a moment fraught with the potential for great change. Mr. Mubarak will have only a brief mourner's respite. The ground is moving and he must hit it running.

In this flux, the United States has special responsibilities. Unquestionably, the first is to keep the Egyptian-Israeli peace process on track. This may not be the automatic choice for the Reagan administration. It sometimes has seemed to regard Camp David as an expendable Jimmy Carter relic, and it has focused its attention largely and directly on the military aspect of American strategic interests in the Persian Gulf. It would be tragic, however, if the United States failed to do its utmost to keep Camp David alive. A rare and precious opportunity for peace would be put at jeopardy and the countries of the area could not soon be expected to put stock in any other American diplomatic venture.

If the United States is to protect and profit from its investment in the one Middle East peace process that is actually working, however, then the administrati on cannot sit on the sidelines of the Israeli- Egyptian talks on Palestinian autonomy as it now is. Instead, it must bring its great influence to bear to ensure that Prime Minister Menachem Begin makes good on his Camp David pledge to grant a real enough measure of self-government to West Bank and Gaza Palestinians so that they join the process, accept autonomy and move on to negotiate the "final status" of the occupied territories.

While Anwar Sadat was alive, the administration sometimes seemed to take him and the Camp David framework for granted, as though no particular political exertions were required to keep Egypt content and to make peace work. That was a dangerous attitude then, and it is an impossible one now. In the new uncertainty, only a fresh Reagan commitment to Camp David, however difficult that may be to make good on, can spare American interests the great additional risks that are otherwise surely in store.