This is very very very old (not the link, but SSSS). I wonder why did it pop in HN today.
When I first learned about SSSS, I asked my professor after class why it wasn't invented earlier. He replied that even thinking of trying something like SSSS first requires the insight that you can encode arbitrary data in numeric form, which only became obvious after the invention and proliferation of computers. Which, I suppose, is a good, concrete example of the notion that "a change in perspective is worth 80 IQ points" (Alan Kay).
While that's as good an explanation as any, I still suspect some clever 19th century mathematician could have come up with it as a way to protect e.g. the combination to a safe. Perhaps it was independently invented, but just never shared with the outside world. The whole notion that cryptography is a field of mathematics where results can and should be published to the world is, in itself, a bit recent, given the intense secrecy around the field as late as the Second World War.
His Incompleteness results show that you can essentially write "This statement is false" as a number and blow up the grand project of formalising all of mathematics as a single (edit: typos) infallible, provable monolith.
If that's the key insight you could do SSSS before any actual digital computers were built (those happen very slightly after Kurt Gödel does this work and Turing et al build on it)
The time window between Gödel's incompleteness theorems and the first digital computers seems to be roughly 1931 to 1946 (if you count ENIAC as the first). That very, very closely overlaps with the Second World War--and even the years before the war were treated by many governments as exactly that, years to prepare for war. I suspect that would put a damper on publishing any interesting results in cryptographic techniques, though to be fair, there is also no evidence that anyone secretly, independently invented SSSS during that period or during the 24 years afterward.
Specifically, that's something like the first two thirds of his incompleteness proof spent establishing that as a fairly novel result, followed by rigorous mathematics to the effect of "Given a formula P(x,y) that asserts "We can't prove x(y,y).", can we prove P(P,P)?".