What does a first sentence need to do? Set the scene, make a promise, open a door into a story, entice the reader to continue. This sentence rocks it. "End of the world" raises the stakes to the top of the scale. We know this is an apocalyptic situation – this story will take place at the end and with enough scope to cover the entire world – a strong setting, a strong promise, and a strong draw to see what happens next.
But the end of the world on its own could seem overdone. Look at how the narrator undercuts that. "Let's start" – what could be after the end of the world? That creates more curiosity and drive to continue. Then "why don't we?" – a phrase that shows a certain attitude from the narrator to the audience, a little archness or playfulness, an assumption of familiarity.
Yes, I definitely want to read on after this sentence. The combination of high stakes and defined voice, in just a few words, shows writing craft at a very high level.