Optically addressable spins are actively investigated in quantum communication, processing, and sensing. Optical and spin coherence lifetimes, which determine quantum operation fidelity and storage time, are often limited by spin-spin interactions, which can be decreased by polarizing spins. Spin polarization can be achieved using optical pumping, large magnetic fields, or mK-range temperatures. Here, we show that optical pumping of a small fraction of ions with a fixed-frequency laser, coupled with spin-spin interactions and spin diffusion, leads to substantial spin polarization in a paramagnetic rare-earth doped crystal, Yb-171(3+): Y2SiO5. Indeed, more than 90% spin polarization has been achieved at 2 K and zero magnetic field. Using this spin polarization mechanism, we further demonstrate an increase in optical coherence lifetime from 0.3 ms to 0.8 ms, due to a strong decrease in spin-spin interactions. This effect opens the way to new schemes for obtaining long optical and spin coherence lifetimes in various solid-state systems such as ensembles of rare-earth ions or color centers in diamond, which are of interest for a broad range of quantum technologies.