Did the first cell self-replicate or was it multiple first cells?
Good question. Simple answer here: we have absolutely no idea.

I would hazard a guess to say that the first proto-cell probably did not have the ability to replicate, so there must have been many proto-cells prior to the occurrence of the first true cell with the property to replicate itself with some degree of fidelity. Whether or not at some point cells existed that could be traced to two or more independent abiotic generations, that is unknown. The likelihood of this event is all we can talk about. I defer to biochemists working on this (still very open) problem, but I think it is honest to mention that they too have no idea, really. This is because, as we can surely appreciate, likelihood and outcome are two entirely different things. And unlikely events happen all the time. Each life form and individual is astonishingly unlikely, but historical contingency so happens to have brought us all here despite the odds.