The Probabilistic Digital Twin framework for geotechnical design and construction, introduced by (Cotoarbă et al., 2025), enables the explicit representation of uncertainty through probabilistic modelling and Bayesian inference, allowing system states to be updated as new observations become available. Despite its conceptual advantages, practical implementation of Bayesian inference in engineering remains challenging, as it typically requires repeated evaluations of high-fidelity prediction models such as finite element analyses, which are computationally expensive. Surrogate models have been proposed as efficient alternatives to such high-cost simulations. However, most surrogate modelling approaches assume stationarity and neglect temporal variability. This limits their application in the context of digital twins, where system states, parameters, and data evolve over time, potentially causing surrogate models to lose accuracy as the system moves through the parameter space. In this work, we propose a sequential surrogate modelling workflow for Bayesian inversion within probabilistic digital twins. The proposed approach combines Gaussian process surrogate models with active learning strategies and efficient Bayesian updating techniques, enabling the surrogate model to evolve in parallel with the digital twin as new observations are integrated. By adaptively improving surrogate model predictions only where needed, the framework maintains predictive accuracy while controlling computational cost. The proposed workflow supports self-learning and adaptivity for digital twins operating in uncertain, dynamic environments. By ensuring reliable probabilistic inference over time, the approach contributes to building trust in digital twin methodologies for engineering design, monitoring, and decision support.