It was a culmination of efforts by many scientists and engineers, particularly those working on rocketry during the Cold War space race. While Sputnik 1 itself was designed and built under the leadership of Sergei Korolev, it was the work of many Soviet scientists and engineers that made it possible.
It's important to note that the term "space probe" is often used to refer to spacecraft that travel beyond Earth's orbit, and Sputnik 1 was primarily designed to test orbital mechanics. The first probe to actually fly beyond Earth's orbit was Luna 1, also launched by the Soviet Union in 1959.
