Eliminating soluble boron in small modular reactors (SMRs) offers several advantages such as an enhanced negative moderator temperature coefficient, reduced corrosion, and a simplified chemical and volume control system. These benefits lead to an increased interest in soluble-boron-free (SBF) SMR. However, soluble-boron-free (SBF) cores rely on burnable absorber at beginning of cycle (BOC) and control rods movements throughout the cycle for the operational reactivity control, potentially leading to higher power peaking and increased fuel failure risk during operation. Therefore, a comprehensive core design is crucial to ensure operational safety and fuel integrity under operating conditions. This research starts from an academic SBF Karlsruhe Small Modular Reactor (KSMR) core, which was developed at BOC in a generic light-water SMR. To optimize its performance with burnup, this research used the lattice physics code CASMO5 and the core simulator code SIMULATE5 to conduct the first-cycle core depletion simulations. By optimizing the radial fuel assembly layout and control rod movement patterns, the core depletions were iteratively performed to identify an optimized design that meets the design targets and safety criteria. This first-cycle core design serves as a valuable starting point for developing a multi-cycle SBF SMR core.