I don't have any veneer of certainty about how life emerged from prebiotic inert chemicals.
The answers are far from certain, and that is precisely what makes it such an interesting scientific question.
It actually didn't take billions of years for life to emerge from a prebiotic state. As best we can tell, the first cells emerged a few hundred million years after the heavy bombardment phase, only relatively shortly after Earth's environment became relatively stable.
The first complex multicellular creatures with hard parts and shells seem to have exploded onto the scene from single celled precursors in the span of only about 30 million years.
These spurts of biologic emergence is a vexing and endlessly interesting scientific question.
On the other tangent, I don't think the word complexity truly captures the intractable problem of abiogenesis. Inorganic and organic systems can have the properties of complexity.
What makes life peculiar is that even at the level of an individual cell we see self organization, a seemingly choreographed dance of organelles and parts, self reproduction, and an infinitely complex system of information transmission and replication. I still remember thinking in introductory biology and genetics classes that a single cell seems like a maddeningly complex and choreographed system of self organizing machinery.
That is what makes it so bloody fascinating, and such a fruitful avenue of scientific inquiry.