As the demand for sustainable material solutions to address climate change intensifies, the development of energy-efficient materials has become a major focus of research. Transparent conducting materials play a central role in this effort, with silver nanowire networks emerging as promising candidates thanks to their flexibility and low material consumption. In this study, we introduce fundamental concepts from percolation theory to investigate the complex behavior of these intrinsically disordered, nanoscale systems. We then present the original concept of bridge percolation, a novel mechanism by which sparse nanowires restore conductivity across fractured thin films. Using high-performance computing, we validate a predictive, parameter-free model that captures this phenomenon and reveals the potential for ultra-low material use. This work offers both theoretical insight and practical pathways toward next-generation, sustainable transparent materials.