Around 10% of newborns require some help to initiate breathing, and 5\% need ventilation assistance. Accurate Time of Birth (ToB) documentation is essential for optimizing neonatal care, as timely interventions are vital for proper resuscitation. However, current clinical methods for recording ToB often rely on manual processes, which can be prone to inaccuracies. In this study, we present a novel two-stream fusion system that combines the power of image and video analysis to accurately detect the ToB from thermal recordings in the delivery room and operating theater. By integrating static and dynamic streams, our approach captures richer birth-related spatiotemporal features, leading to more robust and precise ToB estimation. We demonstrate that this synergy between data modalities enhances performance over single-stream approaches. Our system achieves 95.7% precision and 84.8% recall in detecting birth within short video clips. Additionally, with the help of a score aggregation module, it successfully identifies ToB in 100% of test cases, with a median absolute error of 2 seconds and an absolute mean deviation of 4.5 seconds compared to manual annotations.