The drilling of non-vertical wellbores requires effective real-time monitoring techniques to improve drilling efficiency. This study innovatively develops nine robust hybrid machine learning (HML) models to develop a real-time surrogate model for the drilling cuttings transport index (DCTI). The DCTI, a comprehensive indicator of hole-cleaning efficiency, is typically calculated with a 2-4 h delay due to its dependency on laboratory-measured fluid properties. Our hybrid ML models overcome this limitation by accurately emulating the DCTI value using only real-time, surface-recorded drilling data. A 6818-record dataset was collected from three oil and gas fields (Eastern Province of Saudi Arabia), comprising three offshore and two onshore wells. Following a meticulous dataset preprocessing, a nondominated sorting genetic algorithm (NSGA-II) was applied with a multi-layer perceptron neural network (MLPNN), identifying seven key features influencing DCTI - inclination angle (ANG), rate of penetration, flow in, depth, torque, stand-pipe pressure (SPP), and revolutions per minute. Extreme learning machine (ELM), MLPNN, and radial basis function neural networks (RBFNN) were hybridized with particle swarm optimization (PSO) and a growth optimizer in two stages: (1) to determine the optimal model structure, and (2) to fine-tune the model hyperparameters to precisely estimate DCTI based on the selected features. The HML models achieved better estimation performance and generalizability than the standalone models. Achieving the lowest root mean square error (RMSE = 0.00344), the RBFNN-PSO model exhibited the best DCTI estimation performance. Analytical scoring, robustness, and Monte Carlo simulation confirmed this model's superior performance, robustness, and high generalization. Shapley additive explanations (SHAP) feature influence analysis revealed that ANG exerted the most influence on the RBFNN-PSO estimations, while SPP had the least impact. During drilling operations, the proposed data-driven approach practically enables drilling crews to diagnose and monitor hole-cleaning performance in real time and improve the rate of penetration. Furthermore, SHAP analysis transforms the model into a prescriptive tool, identifying the primary real-time parameters affecting hole cleaning. This enables drillers to make targeted operational decisions, such as adjusting the rate of penetration or flow rate, to mitigate developing issues.