How do I even address an axiom that says the universe has always existed if I don't know what theories are out there
No, you're missing the point.
An axiom is something that cannot be proven (in the mathematical sense) to be true, but is
self-evidently true and accepted as such by everyone.
Your "axiom" was not self-evident (in that someone, anyone, could simply say "I can't see that"),
nor was it true
because there are conflicting data/ theories.
That is what a personal cosmology is about, one man’s personal ideas
So it's a personal view.
And will never be anything more.
You see my dilemma? I either have to sacrifice a complete, consistent and connected physical picture of the universe, i.e. my personal cosmology (which is not an option) or I have to have statements about what is self-evident to me even if they don't stand up as axioms.
There's the
fundamental problem. The statement "which is not an option" regarding abandoning your personal view.
That makes it simply your individual dogma.
Not science, not protoscience, but dogmatic pseudo-science and a refusal to face facts.
You think a real scientist wouldn't give up his view of things if shown that it didn't conform to known facts?
Hell, I've lost count of the number of projects I've worked on (consuming thousands of man-hours* and tens of thousands of pounds of real money, not to mention that that time and money could have been used on something else) just to have someone turn up and say "We had another look and X is a real problem, it will never work".
Should I have said "Fuck you, I've put too much time and effort into this to give up and even though it won't work I'm carrying on"?
Being wedded to a personal view simply because it's personal and you've put time into it means nothing
whatsoever if it goes against the facts.
That's part of life.
And NOT junking the rubbish to start again with something (hopefully) better is nothing more than than throwing good money/ time/ effort down the drain with the bad.
That's just compounding the folly.
You learn that shit happens, keep the good bits (if there are any) and lose the rest.
* Not just my time either.