The Golden Rule has been part of morality for thousands of years. One famous formulation is “What is hateful to you, do not do to your fellow: this is the whole Torah; the rest is the explanation; go and learn.” (credited to Hillel the elder. See https://infogalactic.com/info/Golden_Rule#Judaism)
Given the validity of the Golden Rule, we can prove the NAP very simply:
1. NAP requires only that you don’t force anyone to do anything (or to refrain from doing anything).
2. It is logically impossible to want to be forced to do anything (or to refrain from doing anything), as anything you are willing to do (or refrain from doing) doesn’t require force to get you to do it (or refrain from doing it).
3. Thus, forcing someone else to do something (or to refrain from doing something) violates the Golden Rule, because you are doing to someone else what you wouldn’t want to have done to you.
Q. E. D.