To say “because of war”, you would also have to prove we could not do it without war.
But when it comes to space technology, if it was possible to produce the same technology by targeting the required technology directly, we can’t say it was because of war only because some of the inventions of war were re-used. It eould be like saying we have a 45th president thanks to Trump - it would be absurd as we’d have a 45th president anyway.
So I do not think there is enough grounds to attribute this mission’s success to war - with some of the war’s budget, NASA could have invented the required technology anyway.