We demonstrate optically pumped dynamic nuclear polarization (DNP) of 29Si nuclear spins that are strongly coupled to paramagnetic color centers in 4H- and 6H-SiC. We observe 99%±1% degree of polarization. By combining ab initio theory with the experimental identification of the color centers’ optically excited states, we quantitatively model how the polarization derives from hyperfine-mediated level anticrossings. In addition, we developed a general model for these optical DNP processes that allows the effects of many microscopic processes to be integrated. Applying this theory, we gain a deeper insight into dynamic nuclear spin polarization. In particular, our findings show that the defect electron spin coherence times and excited state lifetimes are crucial factors in the entire DNP process. These results lay a foundation for SiC-based quantum memories, nuclear gyroscopes, and hyperpolarized probes for magnetic resonance imaging.