The emergence of large-scale quantum computing poses a direct threat to widely deployed public-key cryptosystems such as RSA and elliptic curve cryptography (Akande, 2025; Thompson, 2025). While several post-quantum cryptographic families have been proposed, most remain rooted in linear algebraic or number-theoretic structures that may inherit unforeseen quantum vulnerabilities. This paper proposes Turbo-NAFS, a novel encryption scheme designed for the quantum era based on non-abelian functional structures and adaptive functional superposition. Instead of relying on algebraic inversion problems, Turbo-NAFS employs order-sensitive functional composition, iterative turbo-style transformations, and contextual entropy injections to create structural hardness against both classical and quantum adversaries. The paper presents the design rationale, algorithmic structure, and security intuition of Turbo-NAFS, positioning it as a new research direction for quantum-resilient cryptographic constructions.