Bayesian geophysical basin modeling (BGBM) methodology is an interdisciplinary workflow that incorporates data, geologic expertise, and physical processes through Bayesian inference in sedimentary basin models. Its application culminates in subsurface models and properties that integrate the geohistory of a basin, rock-physics definitions, well-log and drilling data, and seismic information. Monte Carlo basin modeling realizations are performed by sampling from prior probability distributions on facies parameters and basin boundary conditions. After the data assimilation, the accepted set of posterior subsurface models yields an uncertainty quantification of subsurface properties. This procedure is especially suitable for pore pressure prediction in a predrill stage. However, the high computational cost of seismic data assimilation decreases the practicality of the workflow. Therefore, we introduce and investigate seismic traveltime criteria as computationally faster proxies for analyzing the seismic data likelihood when using BGBM. Our surrogate schemes weigh the prior basin model results with the available seismic data with no need to perform expensive seismic depth-migration procedures for each Monte Carlo realization. Furthermore, we apply BGBM in a real field case from the Gulf of Mexico using a 2D section for pore pressure prediction considering different kinematic criteria. The workflow implementation with the novel seismic data assimilation proxies is compared with the complete computationally expensive benchmark approach, which uses a global analysis of the residual moveout in depth-migrated seismic image samples. Moreover, we validate and compare the outcomes for predicted pore pressure with mudweight data from a blind well. The fast proxy for analyzing the depth positioning of seismic horizons developed in this work yields similar uncertainty quantification results in pore pressure prediction compared with the computationally expensive benchmark. Our fast proxies make the BGBM methodology efficient and practical.