There were many, many nuclear proof bunkers and locations made during the cold war, on all sides. Its not particularly difficult to build something capable of surviving a nuclear detonation, often these would be built underground or in the side of a mountain. There are many, many of these facilities, both civilian, military, and government though today, most are abandoned or used for storage.

Nuclear weapons are extremely powerful, but we also know an absolute ton about how they work and figured out its not that hard to build shelter or even whole facility to survive an attack.

The lingering question though is when will it be safe to get out of the bunker, as there may be radiation, although this depends on the specific weapon used and where it detonated.