An emerging challenge in the statistical physics of glasses is to understand how non-equilibrium driving and internal activity, as encountered in biological materials, interact with slow relaxation and memory. Such memory effects are commonly described using the Mori-Zwanzig projection-operator formalism. Here, we develop an alternative route based on an exact correlation identity. This identity yields a generalized hydrodynamic framework at finite wavevectors and frequencies, in which response functions and transport coefficients can be obtained directly from steady-state correlation functions. The resulting theory extends Onsager’s regression hypothesis and Green-Kubo-type relations to nonequilibrium steady states with memory, providing model independent fluctuation-response relations for non-Markovian dynamics. As an application, we consider chemically driven active fluids and show that reaction cycles generate active viscoelastic memory, which can produce a negative storage modulus at finite frequencies. Our results provide a first-principles route for extending memory kernel descriptions beyond equilibrium and offer a general framework for probing the dynamics of active, biological, and other non-equilibrium complex fluids.