Although two-dimensional (2D) hexagonal boron nitride (h-BN) has been synthesized on metal foil by chemical vapor deposition (CVD) for several years, toxic precursors and low pressure are still used during growth. Here, we use Cu foil as the substrate to synthesize large-area high-quality monolayer h-BN films by CVD just with BN powders and nitrogen gas under ambient pressure. A similar growth strategy can also be used to obtain three-dimensional (3D) hierarchical h-BN foam on a copper foam template. AFM nanoindentation tests showed that our grown monolayer 2D h-BN has high Young's modulus (821.4 ± 62.6 GPa) and breaking strength (69.1 ± 4.0 GPa). BNF@PDMS composites showed superelasticity, perfect strain memory and stable resilience after 10 compression cycles, with low stress/modulus. Both the monolayer films and 3D foam composites exhibit excellent mechanical performance and are promising for mechanical sensors. Our results provide a greener and more economical synthetic route for high-quality h-BN products aimed at their practical large-scale applications.