On neutral atom platforms, preparing specific quantum states is usually achieved by pulse shaping, i.e., by optimizing the time-dependence of the Hamiltonian related to the system. This process can be extremely costly, as it requires sampling the final state in the quantum processor many times. Hence, determining a good pulse, as well as a good embedding, to solve specific combinatorial graph problems is one of the most important bottlenecks of the analog approach. In this work, we propose a novel protocol for solving hard combinatorial graph problems that combines variational analog quantum computing and machine learning. Our numerical simulations show that the proposed protocol can reduce dramatically the number of iterations to be run on the quantum device. Finally, we assess the quality of the proposed approach by estimating the related Q-score, a recently proposed metric aimed at benchmarking QPUs.