OK, let's look at earth's oceanic heat vents.
A chemical soup and enough porous rocks down at the bottom of the ocean to operate as reactors powering endothermic reactions.
These are spread across the entire surface of the earth.
If, by chance, some set of reactions occur forming molecules (or groups of molecules) that catalyse their own formation, then you have constrained self-replication.
Once you have this - and you only need it once, there's an exponential (s-curve really) boom in the prevalence of the chemicals in question.
Any changes to these molecules that preserve the self-replicating nature of the soup will be preserved to an extent and those changes that improve self-replication will not only be preserved but will begin to outpace the parents.
If, for example, I stick a little hydrogen on the front of a structure it'll develop the ability to trace along ion lines.
A chemical soup that hunts its own food.
Of course, these mutations can lead to divergence - which eventually leads to a pseudo-competition.
Step by step, piece by piece, complexity builds up.
Structures integrate and develop the ability to funnel 'food' to where it needs to go for transformation.
And if it is possible for this to happen, then given enough time and enough distinct reactors, it is not simply possible - it is absolutely inevitable.