The comprehension and manipulation of the propagation characteristics of elementary excitations, such as excitons and plasmons, play a crucial role in tailoring the optical properties of low-dimensional materials. To this end, investigations into the momentum (q) dispersions of excitons and plasmons in confined geometry are required fundamentally. Due to advancements in momentum-resolved spectroscopy techniques, research on the q-dependent excitons or plasmons in low-dimensional materials is beginning to emerge. However, previous simulations of low-dimensional systems are adversely affected by the artificial vacuum spacing employed in the supercell approximation. Furthermore, the significance of layer thickness in determining the excitonic and plasmonic characteristics of two-dimensional (2D) materials remains largely unexplored in the context of finite q. Therefore, an extensive investigation into the momentum and thickness dependent behaviours of both excitons and plasmons in 2D materials, which are free of the influence of vacuum spacing, is lacking at present. In this article, we develop a restoration procedure to eliminate the influence of vacuum spacing, and obtain a comprehensive picture of momentum and layer thickness dependent excitonic and plasmonic properties of 2D hexagonal boron nitride (h-BN) and molybdenum disulphide (MoS₂). Our restored simulations are not only found to be in excellent agreement with available experiments, but also elucidate the roles of momentum and layer thickness in the excitonic and plasmonic properties of 2D h-BN and MoS₂. We further unveil the dimensionality effect on the dispersion characteristics of excitons and plasmons in h-BN and MoS₂. Our contribution will hopefully promote the understanding of the elementary excitations propagating in low-dimensional materials and pave the way for next-generation nanophotonic and optoelectronic devices.