There’s always the chance that the show just pulls the plot straight from Fallout 4, in which case they could just recreate that prologue pretty much beat-for-beat. Maybe start by following a VAULT-Tec salesman going door to door or prepping a Nuka-Cola brand event the morning that the Great War starts. It was the first game to start pre-apocalypse, and the show could embrace that in its pilot to establish the retro-futuristic world before the bombs start falling.