Supermassive black holes (SMBHs) of $sim 10^9, M_odot$ are generally believed to be the central engines of the luminous quasars observed at $zgtrsim6$, but their astrophysical origin remains elusive. The $zgtrsim$ quasars reside in rare density peaks, which poses several challenges to uniform hydrodynamic simulations. To investigate the formation of these distant quasars, we perform a suite of zoom-in simulations on a favorable halo, with a mass of $sim 10^{13}, M_odot$ at $z = 6$ and a history of multiple major mergers, ideal for BH growth. We test BH seeds of $10 - 10^6, M_odot$, and various accretion and feedback models, including thin-disk and slim-disk accretion. We find, contrary to previous studies, that light seeds of $lesssim 10^3, M_odot$ fail to grow to $10^8, M_odot$ by $zsim 6$ even with super-critical accretion; that the hyper-Eddington mode leads to lower accretion rates than the Eddington-limited case due to stronger feedback, resulting in significantly smaller BHs by two orders of magnitude; and that while the super-critical model boosts the growth of low-spin BHs, for high-spin BHs the mass may be reduced due to increased radiative feedback. Our simulations show that the first $10^8 - 10^9, M_odot$ SMBHs may grow from heavy seeds of $gtrsim 10^4, M_odot$ via Eddington-limited or mild super-critical accretion facilitated by gas-rich mergers and self-regulated by feedback, and they co-evolve with their host galaxies, producing bright quasars such as those at $zsim$6 and ULAS J1342+0928, currently the most distant quasar at z = 7.54.
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