Polymeric materials exhibit highly nonlinear and inelastic mechanical behavior characterized by strong time dependence, rate sensitivity, and hysteresis under finite strains. Accurately capturing such responses within a unified constitutive framework remains a significant challenge, as classical viscoelastic and viscoplastic models typically rely on predefined analytical expressions that restrict their ability to represent complex material behavior across different loading conditions and material classes. In this work, a data-driven inelastic constitutive modeling framework is proposed to describe the nonlinear viscoelastic and viscoplastic response of polymeric materials in a thermodynamically consistent manner. The proposed approach employs a B-spline-based representation of the effective creep rate, extending recent developments in data-driven constitutive modeling. The framework is formulated under finite deformations and ensures essential physical requirements, including convexity of the elastic free-energy contribution, monotonic dissipation of mechanical energy, and robustness under large strain histories. Model parameters are identified using a comprehensive experimental dataset comprising monotonic uniaxial and equibiaxial loading, as well as stress-relaxation and creep tests performed at multiple deformation levels and loading rates. The resulting model accurately captures both transient and steady-state material responses over a wide range of strain rates, providing improved predictive capability compared to traditional phenomenological formulations. By separating elastic storage and dissipative mechanisms within a unified data-driven structure, the framework offers both interpretability and adaptability. The proposed methodology provides a scalable foundation for future extensions toward temperature-dependent behavior, surrogate-based acceleration strategies, and efficient finite-element implementations aimed at predictive simulation of polymeric components under complex loading conditions.