Amateur rocketry is relatively common, although space shots are a considerable engineering effort. A good example is BPS.space (Joe Barnard) on youtube [1], who is making significant progress towards a space shot (over the karman line) and documenting it in detail, though he's definitely not the first to do a space shot. He's doing everything himself including his own solid propellent, nozzles, casings, flight computers, control surfaces, cameras, and flight computer. On the regulatory side, the FAA has a regulatory regime to support these kinds of activities. There are amateur launch facilities like the Friends of Amateur Rocketry [2] in the Mojave Desert that support these kinds of launches, although they do require you progress through successful launches of smaller rockets to get permission to fly larger rockets, so you can't just rock up with a huge rocket the first time.

[1] https://www.youtube.com/@BPSspace/videos

[2] https://friendsofamateurrocketry.org/