The blastocoel is a fluid-filled cavity characterizing early embryos at blastula stage. It is commonly described as the result of cell division patterning, but in tightly compacted embryos the mechanism underlying its emergence remains unclear. Based on experimental observations, we discuss an alternative physical model by which a single cavity forms by growth and coarsening of myriad of micrometric lumens interconnected through the intercellular space. Considering explicitly ion and fluid exchanges, we find that cavity formation is primarily controlled by hydraulic fluxes, with a minor influence of osmotic heterogeneities on the dynamics. Performing extensive numerical simulations on 1-dimensional chains of lumens, we show that coarsening is self-similar with a dynamic scaling exponent reminiscent of dewetting films over a large range of ion and water permeability values. Adding active pumping of ions to account for lumen growth largely enriches the dynamics: it prevents from collective collapse and leads to the emergence of a novel coalescence-dominated regime exhibiting a distinct scaling law. Finally, we prove that a spatial bias in pumping may be sufficient to position the final cavity, delineating hence a novel mode of symmetry breaking for tissue patterning. Providing generic testable predictions our hydro-osmotic coarsening theory highlights the essential roles of hydraulic and osmotic flows in development, with expected applications in early embryogenesis and lumenogenesis.