Applies to the US (and maybe other countries, I don’t know) but I can’t overemphasize how much flight capacity the us military has.
We got incredible access to military jets in USAF ROTC (Air Force officer training in college) even before we got our commissions or had a security clearance. To get on base and the airfield there was a mild background check, but we were essentially civilians in fatigues that had been vouched for by our detachment’s Lt Col. Getting to literally run around the empty deck of a KC135 then pop into the cockpit and (under extremely careful supervision) operate some of the plane’s controls was a surreal experience. I didn’t make pilot and so did’t ever have the chance to fly in the training slot of the two-seater F15 (my dream), but I did get the opportunity to at least put my hands on the controls of several other USAF planes in-fight including a few jets.
You don’t have to be in ROTC. Getting a ride-along in a military jet as a civilian is not as easy as showing up and asking for a rode, but also not impossible. The military has the cash to put up planes for non commercial reasons and they consider these publicity flights a powerful public relations tool.
Every Air Force base has a PR department that is always looking for positive stories. If you can come up with something that would lead to positive PR for the Air Force, they will totally let you ride along on a training run. I met a guy on a C-130 who was doing a ride along because his IT firm had a program where Air Force vets got some special consideration when they applied.