62 miles is 327,360 feet. No air breathing fighter jet is getting anywhere near that altitude.
Current record for highest altitude of a non-rocket-assisted aircraft is the MiG-25 at ~123,000 ft. These US have the F-104 at just over 100M ft, and the SR-71 at 85M officially, but she’s probably been a good bit higher too.
The foxbat and starfighter records are meh though, as both of those were zoom climbs of specially modified aircraft. The SR-71 was one of the normal planes, and just flew at that height.
Theoretically, scramjets are going to top out around 150M,mayybe 200M ft. No airbreother is going to fly in space. There’s no air, duh.