I’m an historical guy, looking at known timelines of invention/discovery.
Godel showed the limit of mathematics – specifically first order algebras if I remember right around 1931.
Others took up on his work and went “around” the issue while acknowledging it:
Church introduced lambda calculus which helped remove an issue with identity, and Turing introduced discrete time (change) as as distinct elements to allow “logic pieces” to work independently of each other except for how they are linked in a time sequence.
These powers became computing as we know.
Computing as we know it needs the ability to change and branch. It is different from adding up a line of numbers as it can work with movements discrete movements of anything symbolic.