During the graphitization of polar SiC (0001) surfaces through thermal decomposition, a strongly bound carbon-rich layer forms at the graphene/SiC interface. This layer is responsible for the system's high electron-doping and contributes to the degradation of the electrical properties of the overlying graphene. In this study, with the aid of photoelectron spectroscopy, low-energy electron microscopy, low-energy electron diffraction, and the density functional theory, we show that if the graphitization process starts from the nonpolar (11 2 0) and (1 1 00) surfaces instead, no buffer layer is formed. We correlate this direct growth of quasi-free-standing graphene over the substrate with the inhibited formation of tetrahedral bonds between the nonpolar surface and the carbon monolayer.