Did the universe come about by chance or by design?
The birth of a child can be an analogy for the birth of the universe.
Does a child come about by chance or by design?
The answer is neither. A child's DNA was not designed by some omniscient being micromanaging the order of their proteins. A child's DNA is not random either. A mother is not surprised by a random color of skin on her child. Nor is she frequently surprised by random numbers and arrangements of limbs. Nor is she disturbed by random quantities of eyeballs, ears, and noses across her child’s body. Nor is childbirth so random that any possible thing, like a unicorn, could be delivered.
The parameters behind the generation of a child are finely tuned. They are tuned towards a telos - the purpose of survival, reproduction, and continued existence of the genes. Because of natural selection, there is a narrow band of finely tuned parameters that allow for genetic success at achieving the goal.
The genetics of a child are not random, nor designed. They are evolutionary. They arise by the necessity of what came before them. They are necessarily half of what the father has and half of what the mother has. A small amount of randomness is mixed in in the form of mutation, but this is small enough that we don't see random colors, random limbs, and random eyeballs very often.
If you go back in time, you can trace the genetic necessity to grandparents, and then further back to mammalian ancestors. Going all the way back, we trace their genetic necessity to primordial life - the chemical soup that randomly creates the first cell.
But it would be inaccurate to say that the birth of a child is completely random because the initial conditions 4 billion years ago were highly random. It would be inaccurate to say that if no one designs children then each child could randomly be anything, maybe even a unicorn!
Just as children are neither random nor designed, it is likely that the universe is neither random nor designed. If everything has a cause, even the universe needs a cause. There is probably a chain of universes going backwards in time, each the parent of the next. Maybe the most primordial universe was highly random like the first cell. But just as selection pressures created evolutionary necessity upon the structure of life, selection pressures may have created evolutionary necessity upon the structure of universes.
All universes that have bad laws of physics self-implode before reproducing via blackholes. If a universe can't reproduce, it will die due to entropy and cease to exist in that form. There will be no one to talk about it. If another universe finds a way to reproduce, and then evolutionarily iterates, it will fine-tune in the direction of surviving entropy long enough to reproduce.
If the universe is finely tuned, that is not proof of design.
We have evidence of naturalistic evolutionary fine tuning. We have no evidence of divine fine tuning.
Design is a more difficult standard to prove. Design involves agents that have goals. If you want to prove design, you must first build a model of the agent by articulating its capacities and goals. Once you know their capacities and goals you will be able to make predictions about their actions. If the God agent has a goal of maximizing human life and they have all power, then we can predict that human life will be ubiquitous. When we go out into the universe to do our observations, we find that human life is not ubiquitous. The predictions of the design argument fail.
Does this mean that just any type of universe can be created? Is there a universe full of unicorns flying around? And another universe where Islam is the correct religion? That would imply the possibility of much more randomness than should be granted.
Not designed. Not highly random.
Selected for by the pressures of necessity.