It depends on what you mean by "winning the Cold War." Economically? Technologically? Geopolitically? In any case, I'd argue that in the 1950s there was no clear leader.

On one hand, you have the USSR. Though still reeling from the losses of World War 2 and suffering under the increasingly paranoid rule of Stalin until 1953, the USSR also had a lot going for them. The establishment of the People's Republic of China in 1949 was by many seen as an early and catastrophic failure of "containment," and it gave Russia a powerful ally in Asia to guard the east in the event of war. Russia's first successful nuclear test in late 1949 also sent shockwaves through the West, as America's nuclear monopoly was a centerpiece of its strategy in the event of an early war with the Soviets. On top of this is the matter of the Red Army. While badly bloodied, it was still a formidable fighting force that could easily threaten the security of continental Europe. Soviet air power was also probably at its relative height in the '50s, as technology stolen or gifted by/from the Germans, Americans, and British enabled the Soviets to build jet fighters and strategic bombers that rivaled (if not outclassed) those of the Americans. Economically the Soviets were growing impressively in the 1950s (though this growth was not sustainable), with their GNP growing at about 5% annually and plundered factories from eastern Germany recouping some of the losses from WW2. Technologically it was during the 1950s that the Soviets pulled ahead of the US in missile and space programs. Overall, they were on solid footing (for the time being) despite the challenges they faced in managing their sphere of influence in Eastern Europe.

The US, on the other hand, saw a lot of success and a lot of failure. The postwar economic and population boom secured America's position as an economic powerhouse. The Marshall Plan brought many European allies back from the brink of collapse. Communism was suppressed in France and Italy. West Germany was successfully rearmed and economically recovered, giving the US a much needed bulwark on the border with Eastern Europe. The same held true for Japan. The Korean War, while at first a resounding failure, was pulled back from the brink and showed that the US was serious in its commitment to preventing the spread of communism. McCarthyism also rose, which is rightfully seen by many as a negative but simultaneously firmly entrenched anti-communist sentiment into American political and cultural orthodoxy. In essence, while the Soviets were making many notable and surprising short term gains, the United States was better positioning itself for long term success.

That's a fairly general breakdown, so if have specific follow up questions feel free to ask and I'll be happy to try and answer. I'd also like to recommend some reading for you, if you're interested. The Cold War: A New History by John Lewis Gaddis is a pretty easy read, and while I have some personal gripes with it it's a solid foundation for understanding the Western perspective. Vladislav Zubok's A Failed Empire: The Soviet Union in the Cold War from Stalin to Gorbachev is also a good read, though a bit more dense. This is going a bit outside the range of your question, but William Taubman's Khrushchev: The Man and his Era is another great read if you'd like to understand the man at the helm of the USSR from 1953 to 1964. Hope this helped!