Parameter identification for path-dependent plasticity is challenging as constitutive responses depend on different loading histories, internal-variable evolution, and coupled material parameters, while repeated exact forward evaluations during optimization can be computationally expensive. This work presents a physics-verified surrogate-assisted framework for inverse parameter identification, using a novel parameter-path-conditioned operator to map material parameters and strain paths to stress responses. Its architecture combines a material branch for parameter embedding, a strain-path branch for loading-history representation, and a causal path-processing network conditioned through feature-wise linear modulation (FiLM), with physics-consistency terms incorporated into the training loss. The neural operator (NO) surrogate is not used for final parameter selection. Instead, it enriches promising candidate parameters, after which the original physical model re-evaluates every retained candidate and selects the parameter vector with the lowest exact physical mismatch. The framework is evaluated using the Chaboche model, the Johnson–Cook model, and a Taylor impact inverse problem based on finite element (FE) simulation. Three NO-assisted search strategies are discussed: random sampling (NO-RS), gradient-based Adam (NO-Adam), and differential evolution (NO-DE). For comparison, the conventional baselines, trust-region reflective least squares (TRF) and direct DE, evaluate the governing model directly. In the Chaboche examples, across 20 independent runs, NO-DE achieves mean exact misfits of 1.784% and 0.524% for 42CrMo4+QT steel and 7075-T6 aluminum alloy, respectively, compared with 1.776% and 0.519%–0.523% for the baselines, while reducing the complete identification time by factors of 5.2–81.6. The Johnson–Cook examples show that the workflow remains applicable to computationally inexpensive explicit constitutive laws; nevertheless, no runtime advantage is expected in this low-cost regime. The Taylor-impact problem extends the workflow to profile data obtained from FE simulations. Across four different examples, the surrogate errors in stresses were lower than those in the Adam objective gradient and stress Jacobian; for 42CrMo4+QT steel, the median values were 6.493%, 15.041%, and 26.443%, respectively. These show that accurate surrogate predictions of stress responses do not guarantee equally accurate parameter gradients. NO-DE avoids reliance on these gradients and provides the best overall balance of fitting accuracy, stability of parameter identification, and computational cost among the tested strategies. Physics-based re-evaluation selects the best retained candidate, but reliable identification still depends on the surrogate search reaching low-mismatch regions.