This paper presents a novel, model-independent mechanism for the formation of primordial black holes (PBHs) within the framework of non-singular matter bouncing cosmology. The model considers a short transition from a matter contracting phase to the Hot Big Bang (HBB) expanding Universe, during which enhanced curvature perturbations on small scales can collapse to form PBHs. These PBHs can have masses within the asteroid-mass window, potentially accounting for all dark matter. Additionally, the enhanced curvature perturbations can induce a stochastic gravitational-wave (GW) background, which may be detectable by future experiments such as SKA, LISA, and ET. The paper explores the dynamics of non-singular bouncing cosmology, including the background and perturbation dynamics, and derives the curvature power spectrum responsible for PBH formation during the HBB era. It then reviews the basics of PBH formation within peak theory, calculating the PBH abundances and their contribution to dark matter. The study also investigates the second-order GWs induced by the enhanced cosmological perturbations collapsing to PBHs, checking their detectability with current and future GW experiments. The curvature power spectrum during the HBB era is found to have a scale-invariant component on large scales and enhanced components on small scales, leading to PBH formation. The PBH mass distribution is analyzed within peak theory, showing that PBHs can form across a wide range of masses, including those within the asteroid-mass window. The paper also discusses the implications of these findings for dark matter and the potential for detecting GW signals from PBH formation. The scalar-induced GW signal is calculated, showing that the GW spectral density depends on the curvature power spectrum and the parameters of the bouncing cosmology. The GW spectra are presented for different values of the parameters $ H_+ $, $ H_- $, and $ \Upsilon $, with sensitivity curves of future GW experiments superimposed. The results indicate that the GW spectral abundance scales as $ f^2 $ at low frequencies and decays at a UV cut-off frequency related to the non-linear cutoff in the curvature power spectrum. The paper concludes that non-singular bouncing cosmology provides a viable framework for PBH formation and GW detection, offering new insights into the early Universe's dynamics.This paper presents a novel, model-independent mechanism for the formation of primordial black holes (PBHs) within the framework of non-singular matter bouncing cosmology. The model considers a short transition from a matter contracting phase to the Hot Big Bang (HBB) expanding Universe, during which enhanced curvature perturbations on small scales can collapse to form PBHs. These PBHs can have masses within the asteroid-mass window, potentially accounting for all dark matter. Additionally, the enhanced curvature perturbations can induce a stochastic gravitational-wave (GW) background, which may be detectable by future experiments such as SKA, LISA, and ET. The paper explores the dynamics of non-singular bouncing cosmology, including the background and perturbation dynamics, and derives the curvature power spectrum responsible for PBH formation during the HBB era. It then reviews the basics of PBH formation within peak theory, calculating the PBH abundances and their contribution to dark matter. The study also investigates the second-order GWs induced by the enhanced cosmological perturbations collapsing to PBHs, checking their detectability with current and future GW experiments. The curvature power spectrum during the HBB era is found to have a scale-invariant component on large scales and enhanced components on small scales, leading to PBH formation. The PBH mass distribution is analyzed within peak theory, showing that PBHs can form across a wide range of masses, including those within the asteroid-mass window. The paper also discusses the implications of these findings for dark matter and the potential for detecting GW signals from PBH formation. The scalar-induced GW signal is calculated, showing that the GW spectral density depends on the curvature power spectrum and the parameters of the bouncing cosmology. The GW spectra are presented for different values of the parameters $ H_+ $, $ H_- $, and $ \Upsilon $, with sensitivity curves of future GW experiments superimposed. The results indicate that the GW spectral abundance scales as $ f^2 $ at low frequencies and decays at a UV cut-off frequency related to the non-linear cutoff in the curvature power spectrum. The paper concludes that non-singular bouncing cosmology provides a viable framework for PBH formation and GW detection, offering new insights into the early Universe's dynamics.