No. Sorry, but you are mistaken. Cause and effect is not an axiom, it is not universal - it is known not to apply at the quantum scale.
The wiki page 'axiom of causality' is a PROPOSAL, please read citations before posting them. It is not even suggesting that causality is axiomatic.
You are conflating different things. First of all, cause-and-effect is the basis for the "scientific method", so it
is axiomatic to that process. Yes, it is based on certain assumptions, but that still does
not remove its "axiom" implication.
Secondly, you are also terribly mistaken about quantum mechanics, and are conflating not knowing certain causation versus taking a position that there is no causation. We may not understand why photons may go from a particle to a wave or sometimes show characteristics of both at the same time, but that in no way implies there must not be causes for that. It's not that cause-and-effect doesn't apply, it's just that we're far from understanding what the cause(s) may be. Your position would have it that if we don't know what the weather will be like tomorrow in NYC that there is no cause for the weather in NYC.
Attempting to find cause-and-effect of various natural events is an axiom within science even if you don't want to recognize it as such. That's what we try to do.