This study presents a modeling strategy that combines Volterra series and machine learning to predict unsteady transonic aerodynamic responses over a parametric design space defined by Mach number and angle of attack. The method builds reduced-order models by first identifying linear and nonlinear Volterra kernels from CFD-based indicial responses, using a two-step approach that isolates nonlinear corrections to the dominant linear component. Machine learning algorithms, specifically artificial neural networks and Gaussian process regression, are employed to interpolate kernel coefficients across the parameter space. The models are validated on a 2D aerofoil, and a 3D wing configuration, with results showing that including second-order kernels improves accuracy in nonlinear regimes, and that neural networks generally outperform Gaussian processes. The framework achieves substantial reductions in computational cost compared to full-order CFD while maintaining predictive reliability, particularly in complex unsteady scenarios, making it suitable for design and analysis applications.