Why?
If existence is random then we should see a nearly infinitely larger number of universes, where the question of "Is the universe consistent" is answered with no.
To be clear: random fluctuations in at the quantum level should eventually produce our universe: but the probably of being a thinking being and living in a universe that's anything as complex as ours is infinitesimal.
This is NOT a post-hoc argument "look at all we want though we must have been guided" it's exactly the opposite: a priori sentient life should emerge infinitely more often in much much less complex universes.
There's no natural probability distribution over an infinite set. Saying that X is more probable than Y is meaningless.
To answer your question about the appearance of consistent patterns in our universe, I humbly submit that we have "tuned" our consciousnesses to a particular framework from which we produce our own physical, biological, corporeal patterns by abstracting and reacting to certain patterns from the environment in which we've chosen to dwell. We have "synchronized" our conscious focus with the present moment in order to participate in the universe.
In other words, the patterns themselves are in your mind. Their seeming persistence and relative regularity is a consequence of the co-synchronization of your consciousness with the rest of physical reality.
You are only able to create the physical pattern of
you in this reality because you are to some extent in sync with many deeper physical rhythms of the universe -- the orbits of the planets and resultant terrestrial climate and seasons, the tides and the rotation of the planet, even particular bands of frequencies of light and sound.
In still fewer words, mud puddle fits its hole perfectly. News at 11.