In the lore, the "Zetans" have visited/researched Earth for at least a few centuries (the Mothership Zeta DLC for FO3 has you meeting different characters like a feudal samurai, a cowboy from the old west, and an astronaut from before the bombs dropped). They are not why the world ended though.
Before The Great War, international tensions were at an all-time high, with global resources dwindling to dangerous levels. The US fought a war against China and annexed Canada, which the US occupation was more like turning the entire country into one big internment camp. The real reason why the nuclear apocalypse happened hasn't been explained in any of the Fallout media yet, but it feels like the show is going to reveal it at some point if it didn't already. But that's also not really the point of the games/story of Fallout in general; the tagline is literally "War Never Changes" because it's about human nature.
You should watch the show. It's great and very accessible for someone who hasn't played the games. Plus it might give you the itch to try them out, and they're incredibly fun.

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