Understanding the effects of extreme floods on critical infrastructures such as bridges is paramount for ensuring safety and resilient design in the face of climate change and extreme events. This study develops robust computational and predictive modeling tools for assessing the impacts of extreme floods on the hydraulic response and structural resilience of bridges. A computational fluid dynamic (CFD) model utilizing RANS equations and k-ω Shear Stress Transport (SST) for simulating supercritical flows is adopted to compute hydrodynamic pressures and the water levels on bridge piers of cylindrical and rectangular shapes during a flood event. The CFD model is validated based on the case study data obtained from the Haj Omran Bridge, built on the Khorramabad River in Iran. The numerical simulations consider hydrological conditions and exclude geotechnical parameters and abutment damages. The numerical results are evaluated based on well-established design guidelines. Machine learning techniques, including Extreme Gradient Boosting (XGBoost), Random Forest (RF), and Support Vector Regression (SVR), optimized with Grid Search Cross-Validation (GSCV), are adopted to enhance the accuracy of hydrodynamic pressure forecasting at bridge piers. The XGBoost model exhibits superior performance (R2 = 0.908, RMSE = 0.0279, and E = 3.41%) compared to the RF and SVR models. All the estimated pressure data by XGBoost falls within ±6 percent error lines, highlighting the model's robustness for out-of-range hydrodynamic pressure prediction. Additionally, an optimized Long Short-Term Memory (LSTM) model is adopted to effectively predict free surface flow profiles (i.e. flood depth) over the bridge (R2 = 0.937 and RMSE = 0.083), demonstrating its potential for practical applications of flood depth predictions over bridge infrastructures. The proposed methodological framework outlined in this study can facilitate modeling the impacts of extreme floods on bridges, enabling robust climate resilience assessment of critical infrastructures.