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Atomic variation in the surface topography of thin films can have significant impact on their electronic structure, macroscopic properties, and potential technological applications. Because strontium titanate (SrTiO₃) is a common substrate for growing thin films using Molecular Beam Epitaxy (MBE), we investigate the energetics and kinetics of surface rearrangement during homoepitaxial SrTiO₃ growth. We study two different deposition sequences on a bare substrate terminated with double-layer TiO₂. In the sequential deposition sequence a monolayer of SrO is deposited followed by a monolayer of TiO₂ and in the reverse deposition sequence the order is flipped. The structure of the surface is monitored with X-ray Reflectivity (XRR) while models of the surface are energetically minimized with Density Functional Theory (DFT). Using an XRR data inversion procedure constrained to the DFT calculations allows us to determine interfacial structures more accurately than is possible through experiment or theory alone.  The observed dynamic rearrangement of the surface, including layer swapping and the formation and subsequent rearrangement of surface islands grants insight into specifics needed to design more effective protocols for MBE growth of novel semiconductors and quantum materials.