Designing heterogeneous elastic materials to achieve prescribed effective properties is a canonical inverse problem: one seeks microstructural (topological) descriptors that yield a macroscopic, homogenized elasticity tensor matching a desired target within specified tolerances. In many practical settings, this target is not provided in isolation but together with the elastic parameters of the two constituent phases, which are equally prescribed as part of the design specification. In this work we address the inverse problem with a fully differentiable learning pipeline that couples a frozen forward surrogate model with an inverse neural network. The forward surrogate maps a parametrized microstructure, together with the elastic parameters of both phases, to the resulting effective elasticity tensor obtained by first-order computational homogenization for periodic boundary conditions. The inverse network is conditioned on the desired effective tensor and on the prescribed elastic parameters of the two phases, and it proposes feasible microstructural descriptors that are subsequently evaluated by the forward surrogate. The entire composition is trained end-to-end through differentiable consistency losses, enabling rapid inference and gradient-informed refinement while keeping the physics-informed forward map fixed. Importantly, by explicitly conditioning on the phase elastic parameters and training over a broad range of elastic contrasts and combinations, the inverse model remains valid for almost arbitrary elastic phase properties. This capability to handle widely varying phase parameters without retraining motivates the attribute “Universal” in the title and supports robust microstructure design across diverse material systems.