If you accept that likelihood that our Cosmos is designed and fine-tuned (not just for life but to allow even atoms and molecules and higher more complex structures to exist like stars and planets) then I guess your choice is between pure chance (the Mother Nature Hypothesis and/or the Multiverse Hypothesis) and a designer. If the latter, then your choice is between the supernatural (the God Hypothesis) and the natural (the Simulation Hypothesis). What would Ockham’s Razor suggest? What role might mathematics play?
Actually, there is one interesting variation on the Simulation Hypothesis. It’s the Mind Hypothesis or the Dream Hypothesis. You know how absolutely realistic your dreams can be or the images your mind can conjure up. Of course, those dreams and those images are also a form of virtual reality. Are we the product of someone’s dream-world?
Apart from the pure probability that we are virtual reality beings in a computer-simulated landscape, the next best or second best reason for taking the Simulation Hypothesis seriously is mathematics.
The language of our Cosmos is written in mathematics so our reality is also a mathematical reality. Computer gaming reality is also a mathematical reality. Any “what if” research simulation is a mathematical reality. Therefore, our reality might be as a Cosmos, simulated as a computer game or as a “what if” research scenario.
For starters, consider the entirety of the laws, principles, and relationships in physics is expressible in the language of mathematics and mathematical equations. The same pretty much applies in chemistry and also in the earth and space sciences (astronomy/cosmology, meteorology, geology/geophysics and physical oceanography). The natural world and the biological sciences are also steeped in mathematics.
Why do we get fractals in nature like in some leaves, snowflakes, clouds, lightning, coastlines, broccoli etc?
Pi occurs quite apart from the ratio of a circle’s circumference to its diameter in all manner of ways that have nothing to do with circles.
Why do we get meaningful mathematical ratios going from planetary rotations and revolutions to music (octaves; fourths, fifths, etc.)
Why is the Golden Ratio so prevalent and so pleasing (in the human body and especially the human face) and also crops up often in nature from spiral galaxies, cabbage cross-sections to nautilus shells?
Why is symmetry found in nature at all?
Why are the Fibonacci Numbers (the Fibonacci Sequence being 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc.) so over-represented in nature from cauliflower, pineapples, pinecones, sunflowers, flower petals (especially daisy petals) to even the arrangement of leaves on a stem?
Why is the Cosmological Constant fine-tuned to one part in 10 to the 120th power?
But above all else, why is the Cosmos dominated and described by mathematical equations (not of our making) and relationships? For example, mathematics is highly useful in making predictions.
Predictions that are a bit out of the ordinary have included the evolutionary stages of our Sun as it nears the end of its life; the existence of the planet Neptune (confirmed); the Higgs Boson (confirmed); antimatter (confirmed); neutrinos (confirmed); Black Holes (confirmed); and dark matter (yet to be confirmed).
Predictions on a more routine level include eclipses; conjunctions; lunar and other celestial occultations; and whether or not a rogue asteroid will hit or miss the Earth, and if it will hit, when.
Lastly, why are mathematical equations so well designed that in nearly all cases, the coefficients and exponents are all low-value whole numbers (1, 2, 3, 4, 5) or simple fractions (1/4, 1/3, 1/2)? That defies probability. I see no other logical possibility but that mathematical equation that deals with the actual laws, principles, and relationships of physics, etc. have been well thought out and designed to be as simple as possible. The question is, designed by whom?