You can create a point contact transistor with a great amount of care (and lots of expletives as you try to find *two* sweet spots) as a "Proof of Concept" exercise. The results won't be pretty or robust or offer much gain, although the transistor produced is almost certainly going to show a very high noise level, if it works at all.
Making your own vacuum tube (thermionic valve) is more likely to produce a robust and usable device, given enough care: