Flying multi-engine aircraft with an engine shut down is a routine training and test maneuver, so these aircraft have all been flown a lot of hours with an engine out. The tricky thing about ETOPS is ensuring very high engine reliability (so that the probability of coincidentally having two engines fail on a flight is low) and avoiding failure modes that would affect both engines at once (one of the reasons for a lot of redundancy in electrical systems).

And while technically different rules, ETOPS in practice gets attached to other requirements for transoceanic flights, so ETOPS aircraft often have additional life rafts and other equipment.

There’s a bunch of regulations, but from looking through them quickly I think they start with a bunch of testing and analysis initially to show a predicted rate under the requirement, and afterwards they look at the real-world rate with a 12-month rolling average.