Energetic neutrinos provide a view into the underlying processes of astrophysical particle accelerators, but their weakly interacting nature makes them challenging to detect. Current experiments instrument large volumes of ice or water with 3D grids of photomultiplier tubes (PMTs) to capture the Cherenkov light produced by interactions of high-energy neutrinos. Such detectors must be located in remote locations deep underwater or in ice to reduce atmospheric background signals. These challenging conditions impose strict limits on the power and bandwidth available for data transfer to the surface, and triggers are used to maintain manageable rates. We evaluate the potential of fast, intelligent machine-learning triggers that can be implemented on low-power field-programmable gate arrays (FPGAs). We aim to make the most of the given hardware with improved discrimination of signal and background and therefore improved sensitivity to low-energy events. In particular, we focus on the case of underwater neutrino detectors and the efficient discrimination of track-like signals from the bioluminescence background. We develop a machine-learning trigger by using the planned P-ONE experiment as a case study and implement a software testbench to compare its performance to a less complex trigger design based on coincident detections.