Implementation of many quantum information protocols requires an efficient initialization of the quantum register. In the present paper, we optimize a population trapping protocol for initializing a hybrid spin register associated with a single nitrogen-vacancy (NV) center in diamond. We initialize the quantum register by polarizing the electronic and nuclear spins of the NV with a sequence of microwave, radio-frequency, and optical pulses. We use a rate equation model to explain the distribution of population under the effect of the optical pulses. The model is compared to the experimental data obtained by performing partial quantum state tomography. To further increase the spin polarization, we propose a recursive protocol with optimized optical pulses. We also discuss the role of the relative values of the nuclear- and electronic-spin pumping rate in achieving the maximum degree of spin polarization.