We study experimentally the displacement of one fluid by another in a granular pack to uncover relationships between fluid invasion and medium deformation. We develop an experimental setup that allows us to reconstruct the coupled invasion-deformation dynamics in 3D. We simultaneously characterize the fluid invasion pattern and document a transition from fluid-fluid displacement in pores to the formation of conduits by grain motion. We rationalize the findings in terms of a simple poromechanics model that indeed captures this transition as a result of the balance between viscous and frictional forces. These results contribute to elucidating the role of three dimensionality in the timing, mode, and morphology of fluid-fluid displacement and injection-induced deformation in porous media.