Neural network–based constitutive models have emerged as an efficient alternative to traditional material modeling approaches for nonlinear solids. However, for history-dependent inelastic materials, most existing methods rely on recurrent neural networks or latent internal variables to encode loading history, which makes them sensitive to temporal discretization and dependent on complete deformation histories or carefully initialized hidden states. These limitations hinder robustness in practical applications involving incomplete, noisy, or pre-stressed loading conditions. In this work, we develop a history-aware neural operator (HANO) for modeling path-dependent constitutive behaviors without introducing latent internal variables. The constitutive response is learned as an operator mapping between function spaces governed by hidden dynamics, providing a generic model that naturally extends to inelastic mechanisms such as plasticity and anisotropic damage. The resulting constitutive representation is discretization-invariant, self-consistent, and capable of predicting stress evolution from general pre-stressed configurations without requiring access to complete deformation histories. Furthermore, the constitutive operator is seamlessly integrated into the Neural-Integrated Meshfree (NIM) framework, a hybrid neuro-numerical method derived within a consistent meshfree Galerkin formulation. Implemented in JAX, this hybrid solver is fully differentiable and supports scalable forward simulation, inverse parameter identification, and gradient-based material evolution control through automatic differentiation. The proposed framework is validated on a suite of benchmark problems, including elastoplastic materials and brittle media with progressive damage. Numerical results demonstrate improved accuracy, robustness to incomplete history information, and favorable scalability compared to existing data-driven and physics-informed approaches. By unifying HANO with differentiable meshfree simulation, this work provides a versatile computational platform for data-driven constitutive modeling and hybrid physics–AI simulation in nonlinear solid mechanics.