Jet impingement is widely employed in advanced manufacturing processes due to its superior heat transfer efficiency. For the precise prediction of thermal performance in twin slot jet configurations, the consideration of 3D flow characteristics is required, particularly the end effects and fountain instability governed by the nozzle aspect ratio. However, the application of high-fidelity simulations, such as Large Eddy Simulation or Detached Eddy Simulation, to iterative design optimization is restricted by their high computational costs. To overcome this limitation, a hybrid framework combining physics-based 3D computational fluid dynamics (CFD) and a data-driven machine learning (ML) surrogate model is proposed. Three-dimensional unsteady Reynolds-averaged Navier-Stokes equations are solved to efficiently construct a comprehensive dataset. Through this approach, the physical correlation between the end effects and the modulation of central fountain instability is clarified across a wide range of aspect ratios. Subsequently, a machine learning surrogate model is developed using the acquired dataset. The critical aspect ratio threshold, where the conventional 2D assumption loses validity, is quantitatively identified. Furthermore, a generalized correlation for the Nusselt number is derived as a function of the aspect ratio. A cost-effective engineering tool is provided, bridging the gap between idealized 2D models and realistic 3D geometries, thereby facilitating the design optimization process for industrial applications.