I believe those characteristics are true because Math is a description of the nature of Being. If it exists, then Math describes it.
I'm not a mathematician, but was trained in Physics, which is Math applied to the physical universe that comprises Objective Reality. Or as some have said, Math is the language in which Physics is written.
The fundamental inarguability of Math (and of Physics) is the basis for all else that we do and experience, whether we know and acknowledge it, or not. It is God's Gift to sentient beings.
There's an old (and vaguely profane) joke about what God's occupation must be, based on various parts of the human body. It misses the point. If indeed God has an occupation, then He is a Mathematician. All else follows from that.
Math can be used as a modelling tool for reality to great accuracy but never forget models are simplifications. Models are always at least partly wrong, and sometimes very wrong.
Like God, mathematics is beyond space and time. It has eternal life with no beginning or end. It's an alien world from outside our universe that we can visit but never communicate with.
The unusual conditions that led to the Big Bang must have extremely long odds for ever happening. However when there's nothing available to measure time, everything that can happen, happens all at once. Maybe God created the universe because he needed a clock.