The X-15 did not take off. It must have stuck out its thumb, because it hitched a ride into flight.
On July 17, 1962, Air Force Maj. Robert White took to the air with his X-15 mounted under the wing of a modified B-52. After separating from the mothership, he ignited his plane’s rockets and ascended to 59.6 miles above Earth, setting a new record.
This met NASA’s definition of space at that time, thus earning Maj. White his astronaut’s wings. Two X-15 flights in 1963 would go even higher, surpassing 100 km, the Karman Line generally accepted as marking the beginning of outer space.
The X-15 appears many times in the Moving Image and Sound Branch’s series Moving Images Relating to Military Aviation Activities, 1947–1984 filed in Record Group 342, the Records of U.S. Air Force Commands, Activities, and Organizations, 342-USAF. A compilation of several different flights can be found at https://catalog.archives.gov/id/69876. The X-15 still holds the record for the fastest manned atmospheric flight at 4,520 miles per hour (Mach 6.7)!
Flight 3-7-14 is known in UFO circles for Maj. White’s remark in a post-flight briefing that he had seen an unidentifiable something outside the window. He reported that he saw what looked like pieces of paper about the size of a hand, but strangely they were not flying past him the way frost from the plane’s nose did. Whatever it was he saw, extensive footage from plane-mounted cameras is now available in the National Archives catalog in the three titles linked from the GIFs in this blog post.