Life on Earth was dependent on chemosythesis for the better part of a billion years before photosynthesis was developed. Photosynthesis is really very complex so I think we can rule that out as an initial form of life.

Hydrothermal vents are a great source of chemical energy in the form of hydrogen, hydrogen sulfide, or other chemicals that can be reacted for energy where the come out into the sea. But you could imagine other sorts of chemical energy driven by other geologic or atmospheric processes that life might bootstrap from.

The origin of the energy provided by hydrothermal vents is the internal heat of the planet.

The reduced substances, like elemental hydrogen and hydrogen sulfide, are produced by the oxidation of the iron(II) ions from volcanic rocks, which is converted by water into rust.

The volcanic rocks contain this more reduced form of iron, because they come from higher temperatures, where their constituent minerals are in chemical equilibrium. When the volcanic rocks reach ambient temperature, the volcanic rocks are no longer in chemical equilibrium with water. This source of chemical energy powers the hydrothermal vents and the associated life.

So the conditions for the appearance of life are an internal source of heat in the planet or satellite and some form of volcanism that can bring substances from the hot deep interior to the cold surface.