How close was humanity to a nuclear "apocalypse" before the advent of ICBMs?

how realistic was mutually assured destruction in the 50s/60s before the invention of ICBMs? the cuban missile crisis was as close as we've been (so far...) to nuclear war but my understanding is that it was precipitated because there were *some* medium-range missiles in cuba that could hit *part* of the US mainland, but not all of it.

let's say arkhipov is overruled and the torpedo is fired - it's the start of nuclear war. how likely is it that it would have *actually* led to the total nuclear apocalypse situation that "mutually assured destruction" implies?