The anomalous magnetic moment of the muon is one of the promising sectors for probing New Physics. Recent results from \(g-2\) experiments indicate a possible deviation of about \(5\sigma \) from the Standard Model prediction. The MUonE experiment was designed to precisely measure the hadronic contribution to the muon anomalous magnetic moment, which could increase the significance to at least \(7\sigma \) and thereby confirm potential discovery. Several crucial milestones have already been achieved by the MUonE project, and the results of the ongoing 2025 test run analysis will serve as the foundation for the full-scale 40 station proposal to be implemented after the LHC Long Shutdown 3. However, classical event reconstruction will face a significant challenge due to combinatorial scaling in this final configuration. To address these challenges, the use of Graph Neural Networks (GNNs) is proposed for the pattern recognition stage, as they offer the flexibility to process irregular geometries while maintaining the low latency required for a trigger. This allows for robust track reconstruction even in scenarios where detector hits may be missing, ensuring accurate performance under imperfect or incomplete data conditions. Abstract Published by the Jagiellonian University 2026 authors