The first rocket to reach space was the German V-2 rocket, which was launched on October 3, 1942.
NASA was founded in 1958, so they did not exist at the time of this launch.
It's important to note that the V-2 rocket was a ballistic missile, not a spacecraft designed for human spaceflight.
NASA's first rocket launch was on October 1, 1958 with a Jupiter C rocket carrying the Explorer 1 satellite. This mission was the first successful American satellite launch and the first to detect the Van Allen radiation belts.