Most people who know statistics learned the frequentist version. This gives exact answers, but requires either a correct theory, or a large number of trials. Even so, it can only give the odds for classes, with no ability to speak to individual cases.
The less known Bayesian statistics does not give exact answers, but is usable for single cases. This is like a doctor who does not want to know the class figures for a given disease, but wants to know whether his patient has it. Many dislike Bayesian statistics because it uses estimates. An modifying estimate can be a frequentist answer, provided that form of statistics is applicable.
Note that since we only have evidence for one universe, the Bayesiam method applies.
To apply to the current question:
You start with prior estimates. For this, let us give priors of 20% probability to, alphabetically; Animist, creationist, mindist, naturalist, and to be complete, none of the above. The last allows those who say no meta-narrative (except their own) is possible a place in the list.
If changes are required to come from basic logic and experiment, this is a formalization of the scientific method.
To introduce one piece of evidence.
The assumption is 10^80 atomic particles in the known universe;
Make further assumptions of 10^18 seconds (about 30 billion years);
10^12 events per second for each particle;
yields a total possibility space of 10^110 events. Anything requiring more than this can be considered impossible.
In Darwin's day, he could describe the simple bacteria as slime. Today we can look at and even modify details. Example
McLaughlin, R. N. et al. The Spatial Architecture of Protein Function and Adaptation. Nature. Published online before print, October 7, 2012.
Later research:
Tirka, B. Why poison dart frogs don't poison themselves. PhysOrg September 5, 2017
and,
Wang, S.Y. and G.K. Want 2017 Single rat muscle Na+ channel mutation confers batrachotoxin auto resistance found in poison dart frog. Phyllobates teribilils. Proceedings of the national Academy of Sciences 114(30): 10491-10496.
Which came first, the poison or the immunity?
Researchers used experiments to estimate the ratio of randomly produced protein strings which can make stable folds to those which cannot. The smallest estimate I know is Sauer's work at 1 in 10^63. Doug Axe noted two problems with the work, one which would produce underestimates, one over estimates. His experimental work comes to about 1 in 10^74 for stable folds with worse odds if they are required to be functional.
Assume the actual odds are 1 in 10^55 power. Calculate the odds of getting two or more functional proteins. Apply this to modify each of the five priors. Don't forget that large valley space between the mountain peaks of stable fold ability. Never forget that a thing must exist before it can evolve.
This can be done for many other such things, such as the odds of two inter-functional proteins being in close enough proximity to work by chance plus time. The Bayesian method is a series of approximations to reality.
This can be applied to the quark >particle >atom >molecule >biomolecule >life hierarchy. Each level's properties depend on those of the next lower level. Most periodic table columns have similar results, with minor changes between rows. Without the properties of Oxygen, carbohydrates couldn't exist. Compare these properties to those of sulfur etd. Or just adjust the electromagnetic force constant > nuclear force constant ratio and see the results. AFAIKS the only way to have our functional universe without intelligent design is a multiuniverse with variant basics for each. This is philosophy, not science, since we don't observe any such universes.
It is far too easy to miss basics:
Also, and I once more have to repeat this because apparently it hasn't entered your skull yet: We have ample evidence that chance and time (as moderated by the mechanisms of evolution) can produce astonishing complexity; this article describes one such experiment (TL;DR: A researcher used a genetic algorithm to configure an FPGA over multiple generations until it reached a specified goal, in this case the ability to distinguish between two audio waveforms.
This experiment made the same error that Dawkin's modified alphabetical string thought experiment did: ignoring that specification of the end result and comparison tests are inputs of information, reducing the odds. To address Dawkins, there are many shapes which are not letters: there are many letter combinations which do not form words: there are many word combinations which do not form phrases; etc. The probabilities of a non-functional result are very much higher than getting a functional one, even just on the letter group level.
The elephant in the room is the exponential expansion of combinatorial inflation as the number of requirements for success increases. Those who smuggle functional information into their experiments while insisting on time and chance as the only answer insist there is no elephant. ID proponents don't think that trumpeting sound is some bugler practicing. They don't think those drafts in the room come from an open window. There are even atheists who accept ID.
If you want to say the last is illogical, I agree!
People tend to pick their philosophies for non-logical reasons - the question is whether they have enough faith in logic and experiment to use them to test their ideas. I know where my bias comes from: at age 15 I only went to church because of the family. A Hungarian lady was speaking Wednesday, and mom nagged me into going. I became aware that perfect judgement on me, from largest to smallest action, would condemn me. At the end, the offer was made: "Come forward, and after we have dismissed the service, we will show you from the Bible how to be forgiven." Later I realized this included the unspoken part - perfect forgiveness from the greatest to the smallest sin with God remaining totally honest. They showed me several places - the one that reached me was Isaiah 53:4>5. I went home rejoicing, and still do.
Eventually I realized that trusting God required my best effort at going by evidence - otherwise it would be the insult to God of living a lie. The right is reserved to test anything to see whether proposed evidence against God has any logical or experimental fallacies.
Example: Kurdish independence: The Kurdish people are still in their homeland, they have not left it for generations and then returned. I don't know of any non-Israelite people who have. The low probability is not forming the Israel nation, but remaining a people while exiled over generations.