Glass forming processes present unique challenges for numerical simulation due to the complex temperature-dependent viscoelastic behaviour of glass, particularly near the glass transition temperature. Besides, traditional simulation approaches require significant computational resources, making real-time predictions for industrial applications impractical. This work presents a unified physics-informed data-driven workflow that addresses these challenges through three integrated components. First, we implement EUCLID (Efficient Unsupervised Constitutive Law Identification & Discovery) for automatically identifying accurate viscoelasticity models from experimental data, leveraging full-field displacement measurements. Second, we develop high-fidelity finite element simulations incorporating the discovered material models to accurately capture forming behaviour. Finally, we establish a robust surrogate modelling approach that bridges simulation data with real-world applications by explicitly accounting for measurement uncertainties. Our framework demonstrates how measured data can inform constitutive law discovery, how these laws enhance simulation fidelity, and how simulation results can be efficiently translated into real-time predictions robust to natural perturbations. Results from laser glass bending experiments validate the approach, demonstrating good agreement with experimental measurements while accounting for measurement uncertainties. This workflow provides a pathway toward digital twins for industrial glass forming processes that balance accuracy, computational efficiency, and real-world applicability.