What do you mean by “the appearance of life”? These elements couldn’t make even a single amino acid, so I’m not sure I follow how these molecules could lead to the appearance of life.
All the complex organic molecules require energy for their production and only elemental hydrogen (reacting with the abundant carbon dioxide) or the less abundant carbon monoxide (reacting with the abundant water) can provide that in the absence of living beings.
The original source of energy that produces the free elemental hydrogen is the internal heat of the planet, which creates underground minerals that are stable at high temperatures, but unstable at low temperatures, so when they are exposed by volcanic processes to the water at the surface they are oxidized by the water, so they release the dihydrogen from water.
Since life cannot have existed from the Big Bang, it must obviously have appeared at some point in time after the formation of the planets.
It cannot have appeared in any place that does not provide the energy required for the synthesis of organic molecules, so the place where life has appeared must have included a source of dihydrogen (and carbon dioxide, but this is ubiquitous). Additional requirements are the presence of sulfides of iron, cobalt and nickel, which are necessary as catalysts, and also of water, ammonia and potassium ions (the latter are required to neutralize the organic acids that form much of the living matter; all the cells of all living beings are filled with potassium ions for this purpose). All these conditions are encountered in submarine alkaline vents or volcanic vents.
Wherever there exists air dissolved in the water, including at great depths in the ocean or underground, the bacteria and any other living beings obtain energy by the easier path of using dioxygen (elemental oxygen from the air) to oxidize either organic substances or inorganic substances, like elemental hydrogen or hydrogen sulfide. All such living beings, even if they live in the dark, depend on the solar energy captured by algae and plants, which have produced the free elemental oxygen.
At higher depths underground or in the marine sediments, where there is no longer enough air dissolved in the water, there are only bacteria that can use the energy of the reaction between dihydrogen and carbon dioxide. In some places where there is no air there are also sulfate-reducing bacteria, which use sulfate instead of carbon dioxide, but those are also indirectly dependent on photosynthesis, because the sulfate comes from other bacteria which live where there is air and which create the sulfate by oxidizing reduced sulfur compounds with oxygen from the air.
The use of solar energy did not become possible until at least a few hundred million years after the appearance of life, perhaps only after more than a billion years, because the trans-membrane ionic pumps powered by solar light are extremely complex structures that could not have been created out of non-living substances.
The only known energy source that can cause the appearance of life is the reaction between dihydrogen (elemental hydrogen) and carbon monoxide or carbon dioxide. Carbon dioxide exists in huge quantities everywhere on any planet without living beings (Earth is an anomaly, because most of the original carbon dioxide has been reduced and incorporated in living matter), so what is necessary for the appearance of life is a source of free dihydrogen. A gradient of ionic concentration in water is also helpful.
Such conditions are present where either volcanic gases are released in water or in the so called alkaline vents, where rocks rich in iron are oxidized by water, releasing the hydrogen from water as dihydrogen (this is the "serpentinization" mentioned in the parent article).
Both kinds of conditions are more typical for certain places on the bottom of the ocean, but they can be also encountered under ground, with the condition that there must be water infiltrated through the rocks, without water there is no source of free dihydrogen.