I tend to believe to the theory of Max Tegmark, that we live in mathematical universe. Which says that some mathematical structures exists, we don't know yet which mathematical structures are "basic", therefore existing, and which are "invented" by us. According to that theory, there is infinite number of possible universes, therefore our universe is, by anthropological principle, one of them, with laws of nature expectedly suitable for intelligent life.
Leopold Kronecker said that god created integer numbers, and everything else is created by man. According to that logic, only (positive?) integers are somehow bult-in into reality, in realm above and beyond "universes", perhaps because non-existence of integer numbers would cause some logical inconstancy.
From that point, we can assume, that any projection of integer set is equally "existent". Every way we look at existing object (integers) is equally "right" or "existent". Our universe, therefore, in its deepest level is mathematical function (projection) of integer numbers, which in turn, as an emergent by some additional projection can be perceived like "Level-3 multiverse" (Max Tegmark), which is multiverse of all Everettian possibilities of quantum interactions.
Note that in this model randomness is human invention, in nature itself there is nothing really random going on, only pseudo-randomness, like indexing problem, or insufficient knowledge / insufficient information.
Tegmark made great point, in my opinion, that function which defines laws of nature in our Level-4 universe is definitely "existant", because we can confirm its existence. But, if similar functions, with little bit different parameters or operators are non-existent, there would have to be some magic substance inside our particular mathematical function. That doesn't sound plausible. Also, we don't know what function define our mathematical universe, we are approaching it from two sides: Schrodinger equation and general relativity, but maybe it contain enormously huge numbers (constants) that we simply cannot ever derive from anything.
Side note: I'm sorry for not being yet allowed to comment/answer on your questions re this and other my posts.