Digital inspection of bridges is becoming increasingly important to manage aging infrastructure and limited maintenance budgets. Reliable and rapid estimation of structural actions and condition from routine measurements can minimize closures and improve maintenance planning. Within this context, the Immersive Bridge Analytics (ImBrAs) project aims to develop a digital framework for rapid, data-driven assessment of bridge structures by combining sensor-enriched structural Finite Element (FE) simulations, Artificial Intelligence (AI) and Extended Reality (XR) to enhance bridge inspection, damage prognosis and decision making. In conventional FE analysis, the structural responses such as displacement, strains and stresses are computed for assumed material parameters and boundary conditions to design bridge components and assess the structural safety. For existing bridges, however, responses are measured only at discrete sensor locations, while the underlying key parameters and boundary conditions often remain unknown. The objective is therefore to identify these underlying parameters solving inverse problems by methods known from structural optimization where the FE model is acting as a black box forward simulator and from investigation of Influence Functions (IF). The inverse problems are either treated as regularized, constrained least-squares or transformed to IF. We propose to employ so called adjoint design sensitivities as IF to benefit from already existing theoretical results and corresponding implementations in the context of structural optimization. To mitigate the noise and possible limited sensor density, we quantify uncertainty in the recovered parameters and report confidence estimates alongside point solutions. Initial tests on a small-scale 3D-printed bridge model show good agreement trends in parameter recovery using proposed approaches. First attempts extending these approaches to laboratory scale demonstrator and to an in-service bridge are reported.