Is it legal to launch myself into space?
There may be local or county regulations and you may have to get a permit. Contact your local amateur rocketry club or stargazing association- they may know.
The FAA also wants to know, possible exception if you are staying in class G airspace.
Short answer, no.
Longer answer: With careful planning, a demonstrated knowledge of applicable laws, and more planning, it can be.
In general the FARs are written to protect other people. You want to build a plane and fly it over unpopulated areas, that’s not too hard.
You want to transit airspace other people are using, or fly it where heavy chunks might land on someone else, that’s not fine.
Shockingly, not everyone is glibly willing to be injured to support your amusement.