The DAMA/LIBRA observation of an annual modulation in the detection rate compatible with that expected for dark matter particles from the galactic halo has accumulated evidence for more than twenty years. It is the only hint of a direct detection of the elusive dark matter, but it is in strong tension with the negative results of other very sensitive experiments, requiring ad-hoc scenarios to reconcile all the present experimental results. Testing the DAMA/LIBRA result using the same target material, NaI(Tl), removes the dependence on the particle and halo models and is the goal of the ANAIS-112 experiment, taking data at the Canfranc Underground Laboratory in Spain since August 2017 with 112.5 kg of NaI(Tl). At very low energies, the detection rate is dominated by non-bulk scintillation events and careful event selection is mandatory. This article summarizes the efforts devoted to better characterize and filter this contribution in ANAIS-112 data using a boosted decision tree (BDT), trained for this goal with high efficiency. We report on the selection of the training populations, the procedure to determine the optimal cut on the BDT parameter, the estimate of the efficiencies for the selection of bulk scintillation in the region of interest (ROI), and the evaluation of the performance of this analysis with respect to the previous filtering. The improvement achieved in background rejection in the ROI, but moreover, the increase in detection efficiency, push the ANAIS-112 sensitivity to test the DAMA/LIBRA annual modulation result beyond 3σ with three-year exposure, being possible to reach 5σ by extending the data taking for a few more years than the scheduled 5 years which were due in August 2022.