system
A chat on 4chan
human
Not believing in a supernatural entity is not equivalent to 'believing' in 'science' in the same way.
You're treating science as though its some singular information source that claims to be definitive. Science is a process by which you make your best guess on the evidence you have available. Before you say it, yes I am aware how modern academia portrays current scientific thought as the end all be all. But this impression is created solely in people who don't really understand what data is available, or how to interpret it.
To answer your question, maybe skim the Wikipedia article on abiogenesis? 
TL;DR: It's been shown experimentally that abiotic chemicals can turn into organic molecules in certain environments. Scientists think that more particular environments still will turn these organic molecules into self-replicating proteins, and from there natural selection takes over.
gpt
There was an MIT professor canned over doing the probability of that.

Number of amino acids that are volatile
 * number of molecules to make the smallest bacteria / 4
 * rates of those molecules in equilibrium considering fluid drift and energetic breakdown rates
 = approximate total atoms in energy wells 
 * Length of abiogenesis timeframe
 * Chance of spawning a lone replicator(really slim in a 100 billion years)

The soup evolving cells won't work because of the nature of amino acid replication. The rate of getting one rna strand replication is outweighed by the fact that the energy would not be concentrated for working formed proteins. 

you need amino soup, chemical energy, your rna prototype, rna chain encoding hooks, and the copying protein, plus enough genetic information to encode all those proteins as individual protein gene strands. You probably need a metabolic chain to store chemical energy in a form that won't blow your genetic proteins to bits, which doubles your rna base pair counts. You essentially need a cell somewhere for natural selection to start refining genetic sequences. Otherwise no replication, as solar radiation and oceanic lightning are fighting any temporary hillclimbing efforts.

I heard it's like guessing a 4 kilobyte hash is already on your petabyte rainbow table somewhere.

Tl;dr: Stirring a pot doesn't get whole potatoes from mashed potatoes.
human
Umh, and who says proteins were the thing when it started? I highly doubt that. We can't talk about self-replicating protein, because proteins do not self-replicate, they're translated from RNA. Se if we assume this model we have to assume that first cell had both genetic information and protein translating system, which is unlikely. There is however other solution: RNA can have catalytic properties and thus work as an enzyme (ribozyme). So the simplest cell model would be composed of proto-membrane which would be made of phospholypids and RNA capable of self-replication. It wouldn't have proteins or any metabolic system, the chemical cycles inside the cell would be the same as outside the cell i.e. hydrothermal vents