If you cannot accept NAP from bottom up, it may be also accepted from the top down. As in you don’t need to start with a void and build from there. You can take your current assumptions and use logic to systematically show the inconsistencies in ideology that ultimately lead to the NAP being left standing.
E.g.: Assumptions: 1) Involuntary Taxation good 2) stealing bad
Deconstruction: they are the same thing. Hence, remove taxation.
Assumptions: 1) Regulations good 2) Me hitting neighbor to prevent him from drinking his own piss bad
Deconstruction: they are the same thing. Hence, remove regulations
We take basic human interactions and deconstruct the macro aspect of government to these human interaction basics and show that our instinct to embrace NAP leads us to reject the state.
You do not need to prove the NAP as long as you show that everything else is inconsistent.