A worldwide natural disaster that kills everyone but a huddled few, who then have to repopulate the world? It happens all the time. When biologists analyze the past of a species they often run into what they call genetic bottlenecks, indicating evolutionary events where virtually all of a species were killed or otherwise prevented from reproducing.
For instance, cheetahs had one of these not too long ago. You know how if a human gets a skin graft or kidney transplant, we have to find a relative who's a close enough match and take immunosuppressants so our body doesn't reject the donor organ? A cheetah wouldn't have to do any of that. They had such an extreme genetic bottleneck recently (that is, so few remained) that all the Cheetahs we have now are essentially close relatives.
"Cheetahs are the inbred rednecks of the African savannah." - Jack Hanna
And humans? We've previously talked about the Toba Event, some unknown disaster 75,000 years ago that may have reduced the population of humanity to just 5,000 freaking people.
More than were supposedly on Noah's Ark, sure, but few enough you could have fit everyone left on Earth on board the Titanic.