If it is random, and the universe is infinite, as we assume it to be, it will happen somewhere, an infinity of times, no matter how unlikely the event is. There should be exact copies of you popping into existence somewhere from quantum fluctuations alone.

Current studies are about finding the most likely pathway, rather than knowing whether of not it is possible. We know it is possible because we are here.

As for the technical details, look up "abiogenesis" ( https://en.wikipedia.org/wiki/Abiogenesis )