Not in a cell, but in porous rock around the hydrothermal vents (at the bottom of the ocean).
Given the exponentialish 'population' growth of chemical soup, coupled with the fact that the very low likelyhood of a localised self-replicator forming, by the time second place came about the game would already be over.
Far more likely is preserved 'mutations' to chemical replicators leading to divergent forms of demi-life.
That’s presumably true, but it means there could have been a very large number of losers not just 1. Aka if extremely primitive life showed up once on earth then it might be a rare event, if it happened 100 trillion times then most planets with the right conditions will have some form of life.
If the spread is too wide then the chance of spatiotemporally cohabiting civilizations of distinct origins will be diminishingly small.
But I don't actually think that the planetary parameters that allow for replication are (in any way) specific to earth.
Consider it in terms of reactions per second - take the likelyhood of non-formation of replicators (call it 99.999999999% - because it actually does not matter), to the power of the number of reactors, to the power of the number of seconds since the universe began.
The likelyhood that no self-replicators form rapidly plummets to a vanishing value.
Anyway something more interesting you said was the belief that all life came from a single cell. It’s unclear if all life ever to exist on earth had cells or if they evolved later. Also, we can’t tell if life showed up independently fairly frequently but was out competed or just once.
This is somewhat dependent on how life is defined. Prions aren’t generally considered alive but would have shown up quite frequently due to random chance. The more complex self replicating matter must be to be considered alive the higher the hurdle for life to have formed randomly but the more likely for simpler self replicating matter to evolve into life. Yet, saying evolution of non living mater results in life seems to twist the meaning around unpleasantly.