Neutrinos play a fundamental role in the understanding of the origin of ultrahigh-energy cosmic rays. They interact through charged and neutral currents in the atmosphere generating extensive air showers. However, the very low rate of events potentially generated by neutrinos is a significant challenge for detection techniques and requires both sophisticated algorithms and high-resolution hardware. Air showers initiated by protons and muon neutrinos at various altitudes, angles, and energies were simulated in CORSIKA and the Auger OffLine event reconstruction platforms, giving analog-to-digital convertor (ADC) patterns in Auger water Cherenkov detectors on the ground. The proton interaction cross section is high, so proton "old" showers start their development early in the atmosphere. In contrast to this, neutrinos can generate "young" showers deeply in the atmosphere relatively close to the detectors. Differences between "old" proton and "young" neutrino showers are visible in attenuation factors of ADC waveforms. For the separation of "old" proton and "young" neutrino ADC traces, many three-layer artificial neural networks (ANNs) were tested. They were trained in MATLAB (in a dedicated way -only "old" proton and "young" neutrino showers as patterns) by simulated ADC traces according to the Levenberg-Marquardt algorithm. Unexpectedly, the recognition efficiency is found to be almost independent of the size of the networks. The ANN trigger based on a selected 8-6-1 network was tested in the Cyclone V E FPGA 5CEFA9F31I7, the heart of prototype front-end boards developed for testing new algorithms in the Pierre Auger surface detectors.