In particular, it’s not hard to produce a computable function that isn’t given by a polynomial-sized circuit (parity doesn’t work as it’s polynomial, but you can write one down using diagonalization—it would be very long to compute, but computable in some suitably exponentially bounded time). But P vs. NP is not about this: it’s a statement that exists fully in the world of polynomially computable functions.
In particular, it’s not hard to produce a computable function that isn’t given by a polynomial-sized circuit (parity doesn’t work as it’s polynomial, but you can write one down using diagonalization—it would be very long to compute, but computable in some suitably exponentially bounded time). But P vs. NP is not about this: it’s a statement that exists fully in the world of polynomially computable functions.