Impossible to prove: perhaps. Especially since everything technically is. But reproducing possibilties in the laboratory goes some way to explaining it. But we don't know the exact chemistry of the Hadean/Archean world, and it is likely there were far more organic molecules around. Carbon can quite naturally form complex molecules (at least relative to most others, in terms of carbon we are talking about very simple structures), and once a self replicating one occurs, then evolution kicks in before life has truly begun.
Note: the following is not nesseccarily an accurate haypothsis, but it gives you a good idea. I'm sure you've all heard of phospholipids. The trigliceride with one of it's three fatty acid chains replaced by a phosphorus atom. Phospholipids have a hydrophillic (attracted to water) "head" and a hydrophobic (repelled by water) "tail". So in water they tend to form globules, with the heads on the outside and the tails on the inside. Now, with more lipids they might form a sheet, made from a double layer of lipids (like our own cell membranes). Now sheets would not last, thoey would very quickly fold over into closed spheres. If it happened to envelop a molecule of DNA, then you would have something not unlike a virus. Still not alive, but on it's way.
It is now suspected that the moon had a strong influence on the development of life. Mostly via the tides. (the moon would have been much closer to the Earth then, it has been spiralling away since it formed)
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