In 1957 the USSR launched Sputnik into orbit around the earth. However, this was not the first man-made object to ever reach space. That feat was accomplished in 1942 by a German V2 rocket.
The V-2 missile was the world’s first ballistic missile and the first object to go into space. It was designed in Nazi Germany … it marked a breakthrough in technology that propelled the Soviet Union and U.S. into an arms race and into space.Smithsonian Air and Space Museum – V2 Rocket
In 1942 the V2 rocket reached a height of 85km. Space was defined by the precursor to NASA to be the height at which control surfaces of an aircraft no longer would have any effect. This occurs at a height of 81km.
There are other definitions of where the edge of space is. However, even with these other definitions, rockets and ballistic missiles routinely traveled beyond the edge of space well before Sputnik was launched.