Yes, but not the best ones. By the time the Aggregate-4 (V2) rocket had made it's show on the battlefront, both the Soviet Union and the United States knew and understood the importance of capturing von Braun and his men. While it would be easy to think that with von Braun and the A4's main location being Peenemünde on the Baltic Sea that the Soviets would have captured them all, it was not the case. von Braun and his team knew that the Soviet Union was quickly coming to Peenemünde, and ordered his team south into Bavaria, to avoid capture. By the time the Soviets reached Peenemünde, the rockets were gone, the plans were gone, and only a few spare parts could be found. While von Braun and his team were safe in Bavaria, there was also the Mittelwerk factory in Nordhausen, which was supplied with slave labour from the Mittelbau-Dora Concentration Camp. At the end of the war, it was filled to the brim with A4 Technology, and occupied by the United States. During the post-war negotiations, the area fell under the control of the Soviet Union, and the future East Germany. Under orders from Washington to extract all of the precious rocket technology, the United States picked the area clean of engineers, rocket parts, and other material, before leaving the Soviets with nothing but a few parts and an empty tunnel. von Braun and his team decided to surrender to the United States, hoping to advance his own dreams of the exploration of Space. For the Soviet Union, all odds were stacked against them. The Soviet Union's rocketry team was headed by the talented Sergei Korolev, a political prisoner of Stalin's Russia, who helped spearhead the research needed to allow the Soviet Union access to rockets. Luckily for both Korolev and the Soviet Union, multiple low-level engineers of the A4 Program, who had worked in Mittelwerk, came out to help the Soviets for chances of increased pay and better rations. The highest-ranking engineer the Soviet Union had at their disposal was Helmut Gröttrup, a man who didn't like von Braun all that much, and wished to lead the Soviet Rocket Program. While working in the East under Korolev, he, and a large number of other engineers were swept up in Operation Osoaviakhim, which brought the A4 engineers, A4 equipment and A4 rockets (The Soviets were able to get some former prisoners to help them find hidden parts the Americans did not get to, allowing a few A4s to be built) to Moscow where they were worked on. Painstakingly, the A4 was reassembled from these parts, as new blueprints were drawn up by these workers, before finally, the Soviet Union rolled out the R-1 Rocket, nothing more than a German A4 built by the Soviet Union. In the United States, von Braun and his team were not hard at work on the research they wanted to, instead they were kept under lock and key in Texas, where they were not allowed research, as the rest of the American military worked on the A4 rockets, while von Braun and his team only fired off a few A4s and helped to refurbish them for the United States. This was the result of Operation Paperclip, an operation similar to Osoaviakhim, that brought hundreds of German engineers into the United States. In 1950, just seven years before Sputnik, von Braun was transferred to the Redstone Arsenal, where he and his team began to work on the Redstone missile, which would form the basis of the future Juno, which launched America's first satellite. In the Soviet Union, Sergei Korolev moved forward with his own plans, improving the R-1, to create the R-2, a bigger, taller, rocket that would fly farther than the A4. With the death of Stalin, and the massive build-up of long-range bombers in the United States, Nikita Khrushchev needed a plan to ensure that the Soviet Union was kept safe from any massive attack by the USA. Bombers were expensive, and instead he banked on Korolev to deliver him what he needed, a missile that could deliver a Nuclear Warhead to the United States, and be cheaper than a bomber. This is what prompted the development of the R-7 Semyorka, which became the basis of the Sputnik-1 and Soyuz rockets still used today. Unlike the United States, which did get the lion's share of German engineers, they did not use them right away, while the Soviet Union used what they could, along with their own native talents and political forces. Sergei Korolev pushed for Sputnik to be launched after the ICBM was certified as working, which suddenly thrust the world into the Space Age. Once von Braun was set to task, his team was able to launch Explorer-1. The first man in space, however, was simply a case of the Soviet Union having a better rocket. As mentioned previously, the R-7 is the basis of today's Soyuz, powerful enough to loft a manned spacecraft into orbit. The United States still had no rocket powerful enough to orbit a man, which is why Alan Shepard only took a suborbital flight. Yuri Gagarin beat Shepard into space because of a more cautious tone in the United States. Problems with the launch of a previous Mercury-Redstone rocket had encountered unexpected acceleration, forcing another test of the rocket. In that time, Shepard's flight was delayed, and Gagarin orbited the planet, beating out the United States.

I hope that helped!

Sources: von Braun: Dreamer of Space; Engineer of War / Korolev: How One Man Masterminded the Soviet Drive to Beat America to the Moon / Red Moon Rising: Sputnik and the Hidden Rivalry that Ignited the Space Age / Dr. Space: The Life of Werner von Braun