: The early-age carbonation curing technique is an effective way to improve the performance of cement-based materials and reduce their carbon footprint. This work investigates the early mechanical properties and microstructure of calcium sulfoaluminate (CSA) cement specimens under early-age carbonation curing, considering five factors: briquetting pressure, water–binder (w/b) ratio, starting point of carbonation curing, carbonation curing time, and carbonation curing pressure. The carbonization process and performance enhancement mechanism of CSA cement are analyzed by mercury intrusion porosimetry (MIP), thermogravimetry and derivative thermogravimetry (TG-DTG) analysis, X-ray diffraction (XRD), and scanning electron microscope (SEM). The results show that early-age carbonation curing can accelerate the hardening speed of CSA cement paste, reduce the cumulative porosity of the cement paste, refine the pore diameter distribution, and make the pore diameter distribution more uniform, thus greatly improving the early compressive strength of the paste. The most favorable w/b ratio for the carbonization reaction of CSA cement paste is between 0.15 and 0.2; the most suitable carbonation curing starting time point is 4 h after initial hydration; the carbonation curing pressure should be between 3 and 4 bar; and the most appropriate time for carbonation curing is between 6 and 12 h.