This paper investigates the industrial setting of real-time classification of early media exchanged during the initialization phase of voice calls. We explore the application of state-of-the-art audio tagging models and highlight some limitations when applied to the classification of early media. While most existing approaches leverage convolutional neural networks, we propose a novel approach for low-resource requirements based on gradient-boosted trees. Our approach not only demonstrates a substantial improvement in runtime performance, but also exhibits a comparable accuracy. We show that leveraging knowledge distillation and class aggregation techniques to train a simpler and smaller model accelerates the classification of early media in voice calls. We provide a detailed analysis of the results on a proprietary and publicly available dataset, regarding accuracy and runtime performance. We additionally report a case study of the achieved performance improvements at a regional data center in India.