How life began on Earth is still not well understood. The “RNA world” is one popular theory. In modern organisms, nucleic acids, DNA and RNA, store and transfer information, but proteins do the actual work of catalyzing chemical reactions. But RNA can act as a catalyst, so maybe the first replicating systems involved RNA catalyzing its own replication. However, RNA doesn’t spontaneously form very easily, so it’s not clear how the RNA world would have gotten started. Borate minerals might help but it’s not clear they were around that early.
Another possibility that’s gotten some attention lately involves droplets that grow and divide, instead of just merging into bigger drops.
A different approach to the topic is to work backward from living organisms, to reconstruct the biochemistry of LUCA, the Last Universal Common Ancestor (not quite the same as the first living thing). Recent research on these lines implies that LUCA was a heat-loving microbe that relied on hydrogen as its energy source, suggesting an undersea volcano as a habitat.
However the first organisms got established on Earth, it happened very quickly. Just about as soon as the planet could support life we find chemical evidence for it, from Isua, Greenland (but no fossils yet). This suggests that the origin of life is pretty easy (unless we want to go with panspermia). Mars may have been a more habitable place early in its history, and perhaps Mars exploration will one day solve the mystery of the origin of life in our Solar System.