The NA62 experiment at CERN has the capability to collect data in a beam-dump mode, where 400 GeV protons are dumped on an absorber. In this configuration, New Physics particles, including dark photons, dark scalars, and axion-like particles, may be produced in the absorber and decay in the instrumented volume beginning approximately 80 m downstream of the dump. A search for these particles decaying in flight to hadronic final states is reported, based on an analysis of a sample of 1.4×1017 protons on dump collected in 2021. No evidence of a New Physics signal is observed, excluding new regions of parameter spaces of multiple models.