As for the universe not being random.....
The evidence is pretty much all of science -and all science hopes to be.
Something truly random would be unknowable -magical, if you will.
The whole "nothing is magical and there must be a scientific explanation" thing should suffice.
Decision is the closest thing to true randomness -because it does not need to make sense. Still.... The possible decisions at any point are knowable.
Unless you are saying the universe is magical and science could never possibly know about it -or that decision affected things at some point after the Big Bang (which we know we now do) -the universe became exactly what the universe would become.
It is possible that the big bang essentially produced randomness generators of sorts, but that which is produced can technically be reproduced and is knowable. Randomness is a matter of perspective. If you do not know what will happen, it seems random -the generator of the randomness is not beyond knowing or predicting by its nature, but is beyond our ability to know or predict.
Also to be considered is the level at which apparent randomness applies or is applied.
Let's say the universe is a house. Let's say the house must have certain properties -but other properties are not crucial. It will certainly have walls, windows, a roof, doors, etc... but paint color, roof style, door shape, etc., etc. might be generated "at random".
That which could generate apparent randomness is essentially a decision-maker with no obvious or apparent predictability or reasoning -but as something is produced, it is produced by a technically knowable and predictable process. The fact that we cannot know it or predict it does not make it truly random. Even if randomness generators were produced, their seemingly-random decisions could have been known beforehand if all data could be known and processed -all interactions predicted based on the properties of the things which interact.
Even when knowledgeable decision is applied by an aware and self-aware intelligence which may or may not be based on anything in particular, only so many options are available -decision can only be applied as it can be applied.
We often believe things to be true based on our perspective -and often make incorrect conclusions. We also like to say things that sound cool, but really aren't true.
Time travel is possible.... Things can be in two places at once.... Everything is the right length if you use a stretchy measuring tape...
I agree with some of what you wrote -and wrote so.