I can't tell for sure as I did not witness that, but my impression of the 50s-60s in the USSR was the euphoria of the achievements and an image that the US cannot match the USSR. It was more like: "they won't even dare".
I agree. Also, I remember a joke about those classes was running - what should you do if you see a nuclear explosion? You should wrap yourself in a white bed sheet and start slowly crawl towards a cemetery.In general, people never beleived in the real possibility of the nuclear war.