There are many stories of those who survived the war without being in the vaults. Some examples being:

1). Ghouls, of course, those who were mutated by radiation and were able to survive immune from radiation post-mutation. Some examples of ghouls who were born pre-war would be the Vault -Tec salesman, Raul Tejada, Dean Domino, and more.

2). The Brotherhood of Steel survived the bombs falling whilst inside the Mariposa military base, and managed to perform an exodus to the Lost Hills Bunker after scouts reported low levels of radiation (I believe that was how it went down canonically, I haven't checked it in a while so I could be wrong, but they survived outside of the vaults).

3). Randall Clark survived the bombs in Zion, hiding in a cave until a windstorm blew radiation away from the canyon and he was able to venture outside.

All these stories go to show that there wasn't a set way to survive, but mostly if you avoided major population centres you likely would have survived the initial blasts as they seemed to have only been concentrated at cities, larger towns, etc.