President Carter's initial diplomatic encounter with the Soviet Union over the weapons of nuclear destruction raises a dual challenge, domestic and foreign, that profoundly tests his presidency.

He is determined to convert the challenge into opportunity; to launch his administration boldly and creatively on the road to reduced danger of nuclear war.

Carter is gambling that he can balance off competing domestic fears and hopes about bargaining with the Russians in order to strike a truly significant arms control deal with the Kremlin. Last year President Ford lost a lesser gamble, more in Washington than in Moscow. Ford's failure is assessed in the Carter White House as a political and diplomatic miscalculation, by a weaker, unelected President.

In the aftermath of the aborted attempt in Moscow 10 days ago to draw the Soviet Union into truly revolutionary strategic arms reductions, the Carter administration maintains that both nations now are surmounting the initial shock of rejecting each other's opening moves. The channels of communication are open. But there is no sign yet of any convergence of opposing position.

Interviews at the top echelons of the administration during the past week discloses that:

President Carter is convinced he achieved his initial goal in Washington's "internal negotiations." He set out to show that his drive for "real arms control" could enfold all camps, loosely labeled "hawks" and "doves." This means, especially, the Joint Chiefs of Staff, potential congressional challengers led by Sen. Henry M. Jackson (D-Wash.), plus many "dovish" arms control enthusiasts, some of them deliberately installed in his administration. So far, Carter appears to dominate both domestic fronts.

The internal bargaining inescapably produced an American offer "too large for the Russians to swallow." Said one high Official: "They were bound to choke on it." Others expected the Kremlin "to toy with it; to raise questions and make a counter-proposal," to "agree to study it," or worst of all, "to spurn it out-of-hand." The Soviet Union took the latter, least-promising course, but kept the subject alive for subsequent bargaining.

Despite the recent furor over the threat of "Soviet military superiority," the Carter administration is currently operating from the oppsite premise: that the United States has a compelling technological advnatage and new weapons systems that can force the Russians to accept fundamental changes in nuclear arsenals, or be worse off than the United States if there is no agreement. It is not only the developing, long-range American cruise missile that confronts the Kremlin. The impending new U.S. intercontinental, mobile MX missile, and a far more potent Mark 12A warhead for Minuteman III fixed-site missiles have raised a major threat to Soviet strategy, officials agree. The Carter administration's price for a deal with the Russians to control these weapons is "deep cuts" in force levels and "a freeze" on the technological race.

This would require a drastic change in current Russian forces and strategy. Soviet strategy puts primary reliance on huge, land-based intercontinental missiles; American strategy is based on a "triad" of land, sea and air forces, with primary reliance on submarine-launched missiles. The U.S. plan would require the Russians to follow the Americans toward the sea. The U.S. argument is that far less detctable submarine missile launchers greatly reduce either side's temptation to knock out the opponent's main force by a surprise "first strike."

But in order to bargain with the Russians, President Carter must make some compromises on his opening demands. Simultaneously, the "hawks" who now support his "comprehensive plan" are poised to reverse course if necessary, and challenge Carter if he compromises too much. They are waiting in the wings to block Senate ratification of "too soft" a compromise.

Top U.S. officials, in private, readily concede this double dilemma. Ex-President Ford claims that Carter, "by going public" with his negotiations, already has locked himself in with the "hard liners in the Senate.

Carter strategists hope Ford is wrong, and are attempting to forestall any potential blocking challenge.

Carter planned long in advance to develop his own base of public support for arms control, if needed to override opponents in Congress "should a crunch come." In Defense Secretary Harold Brown, an expert on weaponry and strategic arms limitation talks, the Carter adminstration believes it has a built-in counter for any "internal" revolt.

Secretary of State Cyrus R. Vance has said publicly that the Carter administration will not bargain away "the essentials" of its deep-cut formula. Jackson and other tough bargainers who now support the plan adamantly concur; but the breaking point could be over whose version of "the essentials" prevails.

In private, some of the most influential U.S. strategists are by no means sanguine that the Soviet Union is prepared to make the radical shifts in its strategy and thinking that are required to make a deal.

"This is a very tough decision for them [the Soviets] to make," one senior American policy-maker acknowledged - "even tougher" than the revolutionary decisions which made possible the first SALT agreements in 1972.

Moreover, this is not an ideal time to be asking the Soviets for profound new decisions. Their senior leader, Leonid I. Brezhner, is 70 and ill. His poor physical appearance in Moscow the day he rejected the American proposals stunned those who had seen him in happier, more ebullient days, a year ago.

Once that ebullience was encouraged by the agreement which Brezhnev probably hoped would crown his career - the tentative arms pact he negotiated with President Ford at Vladivostok in 1974. But that one had slipped through the diplomatic netting, and now Brezhnev faced a new team of American negotiators. Especially missing was the familiar Henry A. Kissinger, with his air of secretive intimacy, his wry humor, his titillating tidbits about the foibles of other world leaders, his ability to evoke a shared feeling that the two of them were shrewdly reshaping the world.

Instead of Kissinger, Brezhnev faced the cool, businesslike Vance. Only one familiar face sat across the table - William C. Hyland, a Kissinger associate now on Carter's National Security Council staff. The rest were newcomers, and they spoke for a new kind of American President.

The other Americans who Brezhnev saw were the chief arms control negotiator, Paul Warnke, Philip C. Habib, under secretary of state for political affairs, and Malcolm Toon, the U.S. ambassador whose assignment to Moscow the Soviets sought to block last year. In the anteroom with other officials sat Lt. en. Edward L. Rowny, the Joint Chief of Staff SALT expert and the first general to go to Moscow on such a delegation.

Was their proposal "one-sided," as Foreign Minister Andrei A. Gromyko publicly charged in an extraordinary Soviet press conference March 31, just after the "very disappointed" Vance left Moscow?

American officials insist it will not be, "when it is bargained out," What the United States presented in Moscow, they say, was "an opening offer," with firm conceptual essentials, but open to "reasonable bargaining." It was admittedly built around the American version of strategic equality, "genuine arms control," and reduced risk of quick-triggered nuclear war.

The "quick plan," or "deferral plan," for a temporary, new U.S. Soviet accord is based on the Ford-Brezhnev projections of 1974, 2,400 intercontinential missile launchers and bombers on each side, of which no more than 1,320 could have multiple nuclear warheads.

Totally deferred under this U.S. offer are the two weapons systems most disputed publicly since 1974: the new Soviet Backfire bomber, which the U.S. military claims has range enough to attack the United States and therefore is a strategic weapon (which the Russians deny), and any restraint on the American long-range cruise missile, a technological innovation similar to a pilotles jet plane, launched from air, sea or ground with remarkable accuracy at distances up to and beyond 2,000 miles.

The official objective of this "deferral plan" is to produce some form of agreement before current limits on offensive strategic weapons expire Oct. 3. The United States is far less concerned about that deadline than the Soviet Union, however, which wants to complete that accord by Oct. 3 with firm limits on the cruise missile system.

The Carter administration has offered the Soviet Union less on deferring the Backfire cruise missile dispute than the Russians repeatedly rejected in 1976. The U.S. objective rere is to draw them into the "comprehensive plan" fordeep arms cuts that is the Carter administration centerpiece.

In brief, this plan would cut down strategic forces on each side from the Vladivostock ceilings of 2,400 missile launchers and bombers to a new low of 1,800 to 2,000 weapons. The U.S. plan also would cut the limit on weapons with multiple warheads from 1,320 to a range of from 1,100 to ,1200.

This would cut existing Soviet strategic nuclear forces more than American forces. The Russians now have more and bigger missiles, but the United States has far more multiple warheads already deployed.

Cruise missiles would only be limited by range in the U.S. offer, to 2,500 kilometers, or 1,550 miles, but they would be unlimited in numbers - air, sea or ground launched. The U.S. argument is that they are not strategic weapons, if the Soviet Backfire bomber, and the potent, Soviet SS-20 mobile missile aimed at Western Europe are not counted as strategic weapons either.

What cuts deeper into Soviet strategy, military history and total Kremlin sensitivities, most U.S. specialists agree is the American proposal least grasped by the public. It was the core of Gromyko's public indignation: a heavy slash in the most powerful form of current Soviet weaponry, huge land-based missile launchers, notably the Soviet SS-18 missile.

The American plan would require the Soviet Union to cut the Soviet force of 308 largest land-based ballistic missile launchers to 150. Total numbers of land-based strategic missiles with multiple warheads would be limited to 550 - which is the number of the presently deployed force of American Minuteman III weapons.

In return for this freeze at Soviet expense, the United States would agree to forgo further improvements on all its land-based missile launchers, and abandon developing a new MX missile.The Soviet Union, in turn, would abandon development of its strategic mobile missiles, their counterpart of the MX.

To check the technological arms race, missile test firings would be limited to six a year on each side for land-based missiles, and six for sea-based missiles, or 12 test each year of the projected agreement running to 1985.

But the Russlans are considerably behind in technology and the outcry raised by Gromyko is that this is all a lopsided deal. President Carter, Vance, national security affairs adviser Zbigntew Brzezinski and other U.S. officials deny that, on grounds that while the United States would end up with more warheads, the Russians would retain an advantage, but a reduced edge, in missile power.

One computation by Herbert Scoville, former Central Intelligence Agency expert on arms control, estimates the U.S. advantage in atomic warheads would be 11,930 to 13,230 compared to 5,518 to 7,218 for the Russians. Scoville says this would be roughly balanced off by a Soviet 2-to-1 advantage in larger Soviet missile "throw-weight."

A tentative "guesstimate" by some U.S. experts put the American warhead level advantage lower - 11,500 to 12,000 on the U.S. side, vs. 8,500 to 9,000 for the Soviets, with an overall balance similarly claimed due to larger Soviet missile power.

These calculations use variables, such as how many multiple warheads will be put on missiles, and what is counted in the calculations. One source in the Jackson camp yesteray dismissed the estimates of large U.S. advantage in missile warheads and bombs as "nonsense - and beyond meaningful estimate now in any event."

There are other elements in the U.S. plan which require large departures in Soviet strategy and practice, such as providing "a data base" on existing Soviet force levels. The Kremlin has never done this; all force level figures used in SALT negotiations are American numbers.

At this stage, there are complexities in the U.S. plan which have produced some contradictory official explanatiosn challenging the claim of adequate American staff work. Officials counter that many of these points would be resolved if actual negotiations ever get under way.

For the Soviet Union, major work is required even to assess the ful implications of the American offer. Vance-Gromyko talks, preceded by preliminary exploration, are now anticipated in the May 20-24 period, in Geneva. But the timing is not dazzling propitious, U.S. strategisits concede. Simultaneously, both nations will be preparing for a review conference in Belgrade, in June, on the Helsinki accord, which assures new outbursts of controversy over human rights.