© 2015 American Physical Society. We address the stability of the surface phases that occur on the C side of 3C-SiC(1¯1¯1¯) at the onset of graphene formation. In this growth range, experimental reports reveal a coexistence of several surface phases. This coexistence can be explained by a Si-rich model for the unknown (3×3) reconstruction, the known (2×2)C adatom phase, and the graphene-covered (2×2)C phase. By constructing an ab initio surface phase diagram using a van der Waals corrected density functional, we show that the formation of a well defined interface structure like the "buffer layer" on the Si side is blocked by Si-rich surface reconstructions.