The excess pore water pressure (EPWP) inevitably generated when tunneling with a tunnel boring machine (TBM) in saturated sand reduces the stability of the tunnel face. Accurately predicting spatiotemporal variations in EPWP thus has instructive significance for stabilizing the tunnel face and mitigating the risk encountered during the tunneling process. In this study, two simple surrogate models based on genetic programming were developed and formulated with three selected variables to describe spatiotemporal variations in EPWP during the drilling and standstill cycles using a dataset collected from the Green Hart Tunnel in the Netherlands. They were subsequently combined using a binary variable determined by the TBM’s working conditions. The predictive performance of the proposed models was evaluated by different accuracy metrics. A comparison study of prediction precision for the maximum EPWP in each drilling cycle using the proposed model and 1D linear transient flow model was conducted. Additionally, predictive uncertainty was quantified and assessed using the quantile regression method along with two uncertainty statistics. The results demonstrate that the proposed models can explicitly and accurately predict spatiotemporal variations in EPWP ahead of a TBM with reliability and robustness and can further serve as a tool for TBM operators to use in managing tunnel face stability conditions.