Model parameter estimation is a central challenge in computational science and engineering, linking high-fidelity numerical models to real-world observations. To model granular materials, simulations can be performed at the microscale using particle-based methods or at the macroscale with continuum approaches such as the material point method. However, parameter inference is hindered by (1) the high computational cost of these models and (2) the complexity and high dimensionality of parameter spaces. To address these challenges, we develop data-efficient strategies that combine model-order reduction, surrogate modelling, and iterative Bayesian inference. In particular, we employ reduced-order representations of spatiotemporal fields together with data-driven surrogates, such as sparse regression and Gaussian processes, to emulate physics-based solvers across parameter regimes. These surrogates enable rapid evaluation of model responses and facilitate adaptive sampling in parameter space. Within this framework, we demonstrate how probabilistic and data-driven approaches can be integrated to accelerate parameter inference in granular column collapse. The proposed methodology supports iterative Bayesian updating with reduced computational cost while maintaining fidelity to the underlying physics. This work highlights how combining reduced-order modelling with adaptive, data-efficient sampling can significantly improve the scalability and robustness of parameter estimation in complex geo-engineering systems.