In a direct challenge to a Republican campaign platform that calls for U.S. military superiority over the Soviet Union, Defense Secretary Harold Brown said yesterday that such a notion is both militarily and economically impossible if the Soviets are determined to prevent it.

And, Brown left no doubt that in his mind the Kremlin would never drop out of any stepped-up arms race with the United States even if it meant imposing further hardships on Soviet society.

Thus, the defense chief argued in a speech in California yesterday, a policy of seeking clear superiority would leave no winner. Tather, he said, it would produce an all-out arms race funneling U.S.-Soviet competition "into the most dangerous arena -- the one most likely to lead to nuclear war."

At some point, Brown said. "one side, its resources stretched to the limit, might believe the only way to prevent the other from achieving superiority would be to strike first."

Brown sought to contrast that with what he described as a Carter administration policy of maintaining "the approximate military balance that exists today" as the best way to protect vital U.S. interests, prevent war and promote international stability.

The speech by the defense secretary to the Commonwealth Club of California in Oakland marked the most determined effort yet of the Carter administration to attack the Republicans head-on over how to deal with Moscow on the question of a new arms buildup.

Secretary of State Edmund S. Muskie and presidential national security affairs adviser Zbigniew Brzezinske have recently struck similar themes in interviews with reporters.

While Brown did not use the term "Republican" in yesterday's speech, his prepared remarks made it clear that the White House will use the top Cabinet officers in the election campaign and that President Carter apparently believes it will work in his favor with the public.

The Republican platform reflects the view of presidential nominee Ronald Reagan and many of his top advisers that the United States has fallen dangerously behind Moscow, especially in atomic arms, and must move toward an accelerated buildup aimed at ultimate superiority.

Reagan, in a recent interview with The Washington Post, said he would sit down with Soviet leader if both sides were talking about arms reductions that would really remove the threat to each other's forces. But he has also said that there would be "a great benefit to the United States if we started a buildup . . . to serve notice on the Soviet Union."

Reagan rejected the idea that the Soviets could keep pace, "I think there is every indication and every reason to believe that the Soviet Union cannot increase its production of arms," he said.

In effect, Reagan argues that the Soviets know they would lose a new arms race and thus be more apt to negotiate meaningfully when faced with the prospect of a U.S. buildup.

Brown, indirectly, called those views "unrealistic, simplistic and dangerous."

"The truth is," he said, "that comprehensive military superiority for either side -- absolute supremacy, if you will -- is a military and economic impossibiility if the other side is determined to prevent it."

The costs alone would be "enormous," Brown said, "let alone in the face of a massive -- 30 percent -- tax cut," another allusion to the Republican platform.

"There can be no return to the days of the American nuclear monopoly. It is wishful thinking of the highest order," he said, to believe that the Soviet leaders would "shrink from imposing additional, even unimaginable hardships on their civilian society in order to say in the arms race."