Osmotically-driven surface buckling is a simple method for introducing controlled micro- and nano-scale topography onto material surfaces. To achieve a fundamental understanding of the buckling process and a library of the equilibrium and kinetically-trapped structures that can be attained, we observe the growth processes of a buckling silicate plate rigidly attached to an elastomeric substrate. The primary variable is the lateral extent of the silicate plate which is shown to dictate the location of buckle initiation, and thus the resulting morphology of the final buckled structure. We present a model to qualitatively describe the radial stress profile within the plate, based on both the diffusion-controlled local osmotic stress and the ability of the plate to transfer this stress to the relatively unconfined region surrounding it. These results and insights provide lessons for controlling the order and arrangement of buckled microstructures.