The aim of this study is to investigate how different pressure levels and annealing times affect the local atomic structure and mechanical properties of pure zirconium metallic glasses. Using molecular dynamics simulations with the embedded atom method, we explored how these changes influence the material's inherent characteristics. Analysis of the radial distribution function, coordination number, and Voronoi tessellation revealed a spectrum of structural arrangements in metallic glass formed across a pressure range of 0–70 GPa. Additionally, the glass transition temperature increased with increasing pressure, accompanied by reduced free volume. The annealing process, ranging from 0 to 5 ns on metallic glass synthesized under 0 GPa pressure, showed the coordination number's significance in achieving a glassy state. Regarding mechanical behavior, both elastic constants and moduli showed a progressive increase with rising pressure, while Young's modulus and hardness displayed enhanced values with longer annealing times.