Here is a flight-ready backup of the first artificial satellite to successfully orbit the earth. Since Soviet President Nikita Khrushchev did not have access to Sputnik to show people, he had a scale model to with which he could demonstrate the satellite: this is also on display.
The USSR also beat the United States in getting the first living creature into space. The living creature, Laika, was a dog who fit into the Sputnik II. Laika is also the only living thing from earth that has ever died in space, having overheated during her fourth orbit.
Luna II is the first manmade item to impact the moon. This baseball-sized sphere gave the USSR yet another first in the race to putting a man on the moon. Clearly the Soviets were winning the contest. The item on display at the Cosmosphere is one of only five that were made.
Enos was the United States' entry into getting a living creature into space. A trained chimpanzee was placed into the Mercury-Atlas 5 and launched. The difference between Laika and Enos, however, is that Enos made it back to earth alive.
That division kept the superpowers divided symbolically in Germany, but in reality the separation was made starker with every success. The Soviets lunged ahead again by launching the first man into orbit. This was Yuri Gagarin's only venture into the final frontier, but it forever launched him into the history books. Not only are Gagarin's space suit and helmet displayed at the Cosmosphere, but the very vehicle he rode in is also behind the glass. Other Soviet citizens traveled in Vostok pods, having to parachute to earth, separate from their vehicle, after reentry. These include the first woman in space, who did not know that she was pregnant at the time.