Acoustic emission (AE) is a powerful experimental method for studying discrete and impulsive events termed avalanches that occur in a wide variety of materials and physical phenomena. A particular challenge is the detection of small-scale avalanches, whose associated acoustic signals are at the noise level of the experimental setup. The conventional detection approach is based on setting a threshold significantly larger than this level, ignoring "false" events with low AE amplitudes that originate from noise. At the same time, this approach overlooks small-scale events that might be true and impedes the investigation of avalanches occurring at the nanoscale, constituting the natural response of many nanoparticles and nanostructured materials. In this work, we develop a data-driven method that allows the detection of small-scale AE events, which is based on two propositions. The first includes a modification of the experimental conditions by setting a lower threshold compared to the conventional threshold, such that an abundance of small-scale events with low amplitudes are considered. Second, instead of analyzing several conventional scalar features (e.g., amplitude, duration, energy), we consider the entire waveform of each AE event and obtain an informative representation using dynamic mode decomposition. We apply the developed method to AE signals measured during the compression of platinum nanoparticles and demonstrate a significant enhancement of the detection range toward small-scale events that are below the conventional threshold.