The atmosphere is unstable. Countless millenia of storms have wracked Genesis, lightning strikes fixing atmospheric nitrogen and seeding the oceans with it. The ocean tides work to grind away at the planet's crust, releasing phosphorous, sulphur and other critical elements into the sea.
Natural clay, pitted with small holes, provides a surface. Carbon atoms, split away from their dioxide form, merge under rare high energy conditions to form lipids. Lipids, being naturally hydrophobic, group together to form films upon the clay. In time these films bind together, creating bubbles. The bubbles grow as more lipids collect on the surface, then split apart into new, smaller bubbles.
Sometimes the fixed nitrogen is subject to rare high energy conditions as well, combining with other atoms to form essential acids - amino acids. These naturally bind together, but changes in energy state and the volatility of the environment often cause them to break apart. Where these strings of acids - polypeptides, not even complex proteins at this stage - survive for a time, their shape changes the energy dynamic in their immediate vicinity. Sometimes they will form a shape that encourages other polypeptides to form. These early enzymes form, break and are never seen again.
Over a long enough timeline and with enough simultaneous repeats, unthinkably unlikely coincidences approach certainty. Sooner or later, one of these early enzymes makes its way by simple diffusion (or perhaps by damage to the lipid barrier) into one of the soap bubbles that proliferate near the clay beds. This sheath of lipids protects the protein from damage from the surrounding environment, but small molecules such as amino acids can still diffuse into the bubble. They pass through the sheath, are bound into new poly-peptides. Eventually the bubble cannot sustain everything within it. It bursts... or it splits and starts the process anew.
Proto-cells have come into existence, simple sheaths of lipids around self-replicating enzymes. They lack nucleotides, selectively permeable membranes or any of the other hallmarks of cellular life as we know it. By a technical definition these cells are machines, not life.
We have entered the Protein Age, a hypothetical era before the RNA Age (which is itself a hypothetical era before life made the conversion to the more stable DNA as a coding substrate). Proteins produce themselves or other proteins, but there is no external code which may be read or translated from (that is not itself a protein).
Edit: The science in this is very loose and in some places downright wrong. It is a story that gets across the broad facts, and should be treated as such.