In finite element simulations for structural dynamics, the stability of conditionally stable time integration schemes is governed by the critical time step. Although eigenvalue analysis can provide an exact evaluation of this stability limit, it becomes computationally infeasible for large models. Consequently, in practice, the critical time step is often estimated on element level using heuristic formulas, typically based on a characteristic element length divided by the material wave speed. However, these heuristics are frequently inaccurate and tend to produce non-conservative estimates. Their reliability further diminishes for complex or irregular element geometries, as they neglect numerous factors influencing the true stability limit. More accurate time step estimators can be derived by utilizing the discrete representation of all possible element configurations within a data-based machine learning approach, see Willmann (2022) and Willmann (2025). For this, the eigenvalue problem on element level is reformulated to separate analytically known or easily computable quantities from those that are computationally expensive and, therefore, require estimation. By carefully selecting the input parameters for the neural network, the resulting estimator is computationally efficient while achieving high accuracy. This contribution presents the foundational concepts and extends them to three-dimensional solid elements, with particular emphasis on tetrahedra, demonstrating the adaptability and reliability of the proposed method. We investigate the influence on both simulation robustness and computational performance in real-world engineering scenarios. Overall, this work highlights how machine learning can meaningfully enhance classical simulation approaches.