The associated concept in regulation is a certification (by plane model, e.g. for all Airbus A321) called ETOPS¹ (Extended Operations). The cert applies to twin engines and basically tells you that a plane can fly up to XXX minutes on 1 functional engine only (e.g. ETOPS = 60, then you have ETOPS 120, ETOPS 180 and currently ETOPS 240 is permitted on a case-by-base basis). Note that "ETOPS-180 and ETOPS-207 cover about 95% of the Earth" (how much you can reach while staying 180-207 minutes from an airport at normal altitude/speed).
The rational justification is not merely technical but rather empirical, proven by real-world data. Certifications usually because companies can demonstrate e.g. "N years of trouble-free XXX-minutes ETOPS experience". In other words, we've been doing it for this long and it works so there's statistically ever-less reasons to believe the certification is flawed.
So, despite all the stats you may collect about birds, and physical + ethological models to estimate how much chance there is it will happen twice to a twin engine plane on both reactors before it can land, it would only prove reality: it just doesn't happen. Or not in ways that more engines would solve. (Birds are a bigger problem for cockpit windows, though.)
Now, another additional bit of safety: all jetliner planes have a "fixed-wing" design, allowing "deadstick landing"². From wiki:
> All fixed-wing aircraft have some capability to glide with no engine power; that is, they do not sink straight down like a stone, but rather continue to glide moving horizontally while descending. For example, with a glide ratio of 15:1, a Boeing 747-200 can glide for 150 kilometres (93 mi) from a cruising altitude of 10,000 metres (33,000 ft).
More recent planes are usually ever better (the OG 747 is from 1969!) At the very least it allows the pilot to 'land' on sea and wait for evacuation in zodiacs. So even in the extremely unprobable event that ETOPS failed (the statistical outlier where a plane loses both engines), you'd probably just glide to the ground 100-200km away at most to reach some landing spot.
There are reasons why air travel is so safe, the safest of all, and most of those are empirical, real, tested then validated. That's why it was such a shame what Boeing did to the 737 MAX; and I hope the 777X program yields the safest planes we've ever seen from them, that they actually innovate in that respect.
Safe travels!
[1]: https://en.wikipedia.org/wiki/ETOPS
[2]: https://en.wikipedia.org/wiki/Deadstick_landing