The performance of crop models in simulating various aspects of the cropping system is sensitive to parameter calibration. Parameter estimation is challenging, especially for time-dependent parameters such as cultivar parameters with 2-3 years of lifespan. Manual calibration of the parameters is time-consuming, requires expertise, and is prone to error. This research develops a new automated framework to estimate time-dependent parameters for crop models using a parallel Bayesian optimization algorithm. This approach integrates the power of optimization and machine learning with prior agronomic knowledge. To test the proposed time-dependent parameter estimation method, we simulated historical yield increase (from 1985 to 2018) in 25 environments in the US Corn Belt with APSIM. Then we compared yield simulation results and nine parameter estimates from our proposed parallel Bayesian framework, with Bayesian optimization and manual calibration. Results indicated that parameters calibrated using the proposed framework achieved an 11.6% reduction in the prediction error over Bayesian optimization and a 52.1% reduction over manual calibration. We also trained nine machine learning models for yield prediction and found that none of them was able to outperform the proposed method in terms of root mean square error and R2. The most significant contribution of the new automated framework for time-dependent parameter estimation is its capability to find close-to-optimal parameters for the crop model. The proposed approach also produced explainable insight into cultivar traits' trends over 34 years (1985-2018).