Yes, a first principle is an axiom. It's something you start with that you can't prove, nor is it logic based. An assumption that other parts of your model use but can't prove. It's not the same as a fact, because by its nature it actually can't be shown to be accurate. If it ever IS shown to be accurate by some kind of evidence, then it is no longer a first principle.
If your first principles are wrong, then anything derived from them is wrong.
However, a first principle that there exists an observable reality can't lead to other reliable conclusions without evidence... because choosing that as a first principle means observations are required for other conclusions.