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 1.4x1017\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.4 \times 10<^>{17}$$\end{document} protons on dump collected in 2021. No evidence of a New Physics signal is observed, excluding new regions of parameter spaces of multiple models.