Context. Due to poor observational constraints on the low-mass end of the subhalo mass function, the detection of dark matter (DM) subhalos on sub-galactic scales would provide valuable information about the nature of DM. Stellar wakes, induced by passing DM subhalos, encode information about the mass (properties) of the inducing perturber and thus serve as an indirect probe for the DM substructure within the Milky Way. Aims. Our aim is to assess the viability and performance of deep learning searches for stellar wakes in the Galactic stellar halo caused by DM subhalos of varying mass. Methods. We simulated massive objects (subhalos) moving through a homogeneous medium of DM and star particles with phase-space parameters tailored to replicate the conditions of the Galaxy at a specific distance from the Galactic centre. The simulation data was used to train deep neural networks with the purpose of inferring both the presence and mass of the moving perturber. We then investigated the performance of our deep learning models and identified the limitations of our current approach. Results. We present an approach that allows for quantitative assessment of subhalo detectability in varying conditions of the Galactic stellar and DM halos. We find that our binary classifier is able to infer the presence of subhalos in our generated mock datasets, showing non-trivial performance down to a mass of 5 × 107 M⊙. In a multiple-hypothesis case, we are also able to discern between samples containing subhalos of different mass. By simulating datasets describing subhalo orbits at different Galactocentric distances, we tested the robustness of our binary classification model and found that it performs well with data generated from different initial physical conditions. Based on the phase-space observables available to us, we conclude that overdensity and velocity divergence are the most important features for subhalo detection performance.