Binder jetting (BJT) additive manufacturing enables the fabrication of complex-shaped metallic parts but requires sintering as post-processing to obtain dense parts. The sintering inevitably causes the shrinkage from green body to dense products, resulting in low dimensional accuracy. In contrast, pressure-less melt infiltration (PMI) fills pores in the green body with a liquid metal driven by capillary pressure and fabricates a dense metal matrix composite without severe shrinkage. To consider the applicability of pressure-less melt infiltration to the post-processing of binder jetting additive manufacturing, it is required to clarify the relationship between pressure-less melt infiltration process conditions and the relative density of the composites. In this study, the liquid Mg/solid Ti system was selected because of good wettability and absence of Mg-Ti intermetallic, and the conditions of Ti powder preforms (corresponding to the green body) were focused on. Ti powder preforms with various powder sizes (2300, 410, 140, and 20 μm) and different shapes (irregular and spherical) were cold-pressed at 76, 102, 127, 153, and 178 MPa to fabricate preforms with various relative densities, pore sizes, and pore morphologies to response the similar characteristics in BJT preforms. Mg melt infiltrated into the preforms under constant conditions to fabricate Mg/Ti composites. The structures of the preforms and composites were characterized by sample size measurement, optical and scanning electron microscopy, and X-ray computed tomography. It was revealed that the relative density of the composite increased with decreasing Ti powder size and using spherical Ti powder, whereas the compact pressure exhibited a slight effect. Furthermore, defect volume increased with increasing infiltration height but decreased around the top surface of the sample. Minute observations around defects in the composites revealed that defects were formed at larger pores, and Mg melt was infiltrated into pores above the defects. These results indicated that infiltration velocity varied depending on the flow channel structure, and gas was trapped at larger pores (far from the outside of the sample) where infiltration velocity was low. Using smaller Ti powder decreased the variation in pore size in the preform, resulting in improving the relative density of the composites by suppressing the gas trapping. This study provides a new insight into the pressure-less melt infiltration process as a post-processing of binder jetting additive manufacturing.