We propose a novel cosmological framework in which space-time is modeled as a compressible, dynamic fluid, and the universe is treated as a finite spherical bubble of this fluid expanding into an external void. The expansion of the universe arises not from a cosmological constant or dark energy, but from a pressure gradient between the internal space-time fluid and the surrounding vacuum. This model derives cosmic acceleration, gravitational behavior, and the arrow of time from a single physical mechanism: the dynamics of pressure within the space-time fluid. We formulate the governing equations using classical fluid dynamics and thermodynamics, showing that a pressure-driven expansion can replicate the results of the standard ΛCDM model, including a transition from early deceleration to acceleration. The theory explains entropy increase as a natural consequence of expansion, linking cosmology with time asymmetry. It also provides a physical basis for resolving the Hubble tension and interpreting inflation as a cavitation-like process. Observational compatibility with CMB, SN Ia, and BAO data is addressed, and a removable section highlights the conceptual inspiration drawn from Quranic descriptions of cosmic structure. This framework offers a unified, testable alternative to conventional cosmology, grounded in classical physics.