You’ve got to use an F-22, with zero armaments and as much fuel as you want. The fuel burns fast, in a few minutes, so bring enough to reach full speed. Go as fast as possible. I can get to M.3.4 at 35-40,000 ft. The most important number however is GS (Ground Speed). This must be as high as possible. Use full power for the entire flight and adjust your altitude to reach the highest ground speed possible. Ignore your airspeed, it’s not really important, so long As your not falling out the sky. As the fuel burns, your optimum altitude will increase. Once you are at speed, and have about 30 seconds of fuel left, you need to put the aircraft into a vertical climb quickly, but not violently. If you are too fast you will loose speed. If you are too slow your control surfaces will “die” due to lack of air before you are vertical. Your engines should die during the ascent due to fuel exhaustion, this is fine. The aircraft will also tumble as the air is too thin to offer any aerodynamic stability. The aircraft will follow a ballistic trajectory up to its highest point (the apoapsis) and then fall back to Earth. It can be rather difficult to get the aircraft back under control, but it is possible, so keep trying! The higher up you regain control the better, as it gives more options for landing (remember, you will have no fuel left). The F-22 in this lightweight configuration can glide efficiently for many miles. Select an airport, descend and land.
Also, the altitude I reached in the session you were refereeing to isn’t that high compared to what I’ve achieved more recently. My record is 191,488 ft.