This paper explores the effect of waste rubber grain size on the porosity, modulus of elasticity, thermal properties, and soundproofing performance of polymer composites with different thicknesses (10, 15, and 20 mm). All properties were tested in accordance with European standards, with the exception of porosity, which was measured using Archimedes’ principle. The findings indicate that with a consistent amount of polyurethane glue, finer rubber grains result in composites with higher porosity, leading to a lower modulus of elasticity but enhanced thermal and sound insulation. In contrast, coarser rubber grains produced composites with lower porosity and a higher modulus of elasticity, though with slightly reduced thermal insulation and significantly worse soundproofing. A combination of fine and coarse rubber grains provided a balanced performance, offering both good thermal and sound insulation while maintaining a high modulus of elasticity. Among the thicknesses tested, 15 mm was identified as optimal, combining a relatively high modulus of elasticity, low thermal conductivity, and better airborne sound insulation index. Future research will focus on applying this composite in concrete building products that meet noise protection and energy efficiency standards.