Variably Scaled Kernels (VSKs) have emerged as a powerful meshfree approximation method due to their ability to adapt locally to data characteristics, thereby achieving enhanced accuracy and flexibility over traditional fixed-scale kernel methods. However, the performance of VSKs critically depends on an appropriate choice of scaling function, analogous to a continuous form of the shape parameter in classical kernel methods. Previous investigations suggest that scaling functions that closely reflect the target function's behavior significantly enhance approximation accuracy, yet theoretical validation of this hypothesis has been lacking. This work bridges that gap by rigorously establishing, through analysis of the Lebesgue function, that scaling functions mirroring the target function indeed yield superior approximation outcomes. Furthermore, we introduce a hybrid numerical strategy that leverages machine learning (ML) to automate the selection of the optimal scaling function. Specifically, we employ a discontinuous neural network trained on sample data to directly learn the scaling function. This data-driven, ML-enhanced approach seamlessly integrates classical approximation theory with neural network methods, removing the dependence on user intuition or heuristics. Numerical experiments validate our theoretical claims, demonstrating that the learned scaling function closely approximates the behavior of the target function, leading to consistently improved approximation results across diverse test scenarios. Our hybrid method thus exemplifies a novel, user-independent solution, combining traditional numerical techniques with the adaptive, nonlinear capabilities of machine learning, fitting squarely within the scope of hybrid solvers explored in this mini-symposium.