The following result by Raz (Elusive Functions and Lower Bounds for Arithmetic
Circuits, STOC'08) is aimed at $VP\neq VNP$ (and not directly $P\neq NP$), but it might be close enough for the OP:
A polynomial-mapping $f:\mathbb F^n \to \mathbb F^m$ is $(s, r)$-elusive, if for every polynomial-mapping $Γ : \mathbb F^s → \mathbb F^m $ of degree $r$, Image($f$)$\not⊂$ Image($Γ$).
For many settings of the parameters $n, m, s, r$, explicit
constructions of elusive polynomial-mappings imply strong
(up to exponential) lower bounds for general arithmetic circuits.