This research investigates the neutronic feasibility of a high-performance soluble-boron-free (SBF) small modular reactor (SMR) core based on a new burnable absorber concept called the Burnable Absorber-Integrated Guide Thimble (BigT). Three unique BigT designs were loaded into the core; each BigT design was judiciously ascertained from the core radial power profile to tailor the required reactivity depletion patterns for an SBF operation. The approach is demonstrated to work well as the SBF SMR design exceeds the targeted cycle length while successfully controlling its burnup reactivity swing between 634 and 800pcm throughout most of its operation. This paper also describes the use of hafnium-doped stainless steel as mechanical shim (MS) rods to attain the core criticality. Because the worth of the MS rods is relatively small, insertion and withdrawal of the rods during operation hardly alter the core radial power distributions. The resulting axial power profile, meanwhile, displays a more refined bottom-skewed pattern during the early portion of the irradiation cycle due to partial top-half insertion of the MS rods. This investigation further deliberates on a modified checker board control rod pattern to assure safe cold shutdown of the core. All calculations in this multiphysics assessment of the 3D SBF SMR core were completed by using a 2-step Monte Carlo deterministic hybrid procedure based on the Monte Carlo Serpent and COREDAX diffusion codes with the ENDF/B-7.1 nuclear data library.