<p>This study investigates the bearing capacity factor of circular footings in mountainous areas. A total of 1280 numerical simulations were conducted using the 3D finite element method and the Hoek–Brown failure criterion. Using various design charts, the correlations between the bearing capacity factor and five input parameters were examined: slope angle, intact rock yield, geological strength index, compressive strength ratio, and setback ratio. The effects of these input factors on the failure mechanism are also discussed. Additionally, novel hybrid Adaptive Moment Estimation (Adam) optimizers are proposed for training artificial neural network (ANN) models by combining the whale optimization algorithm (WOA) and sand cat swarm optimization (SCSO). These swarm-based optimization algorithms are integrated into the standard Adam algorithm to optimize both its hyperparameters and the network architecture. Evaluation results demonstrate that the proposed hybrid optimizers outperform the default version. The SCSO-Adam model, which achieved a high accuracy (<i>R</i>² = 99.68%), is proposed as the most effective hybrid Adam optimizer for predicting the bearing capacity of circular footing on rock slopes. A sensitivity analysis was then conducted to evaluate the contribution of each input parameter to the bearing capacity factor. The results of the importance analysis indicate that the geological strength index is the most critical design parameter, followed by the intact rock yield, setback ratio, slope angle, and compressive strength ratio.</p>