  We study the early growth of massive seed black holes (BHs) via accretion in
protogalactic nuclei where the stellar bulge component is assembled, performing
axisymmetric two-dimensional radiation hydrodynamical simulations. We find that
when a seed BH with $M_\bullet \sim 10^5~M_\odot$ is embedded in dense
metal-poor gas ($Z=0.01~Z_\odot$) with a density of $\gtrsim 100~{\rm cm}^{-3}$
and bulge stars with a total mass of $M_\star \gtrsim 100~M_\bullet$, a massive
gaseous disk feeds the BH efficiently at rates of $\gtrsim 0.3-1~M_\odot~{\rm
yr}^{-1}$ and the BH mass increases nearly tenfold within $\sim 2$ Myr. This
rapid accretion phase lasts until a good fraction of the gas bounded within the
bulge accretes onto the BH, although the feeding rate is regulated owing to
strong outflows driven by ionizing radiation emitted from the accreting BH. The
transient growing mode can be triggered for seed BHs formed in massive
dark-matter halos with masses of $\gtrsim 10^9~M_\odot$ at $z\sim 15-20$ (the
virial temperature is $T_{\rm vir}\simeq 10^5~{\rm K}$). The host halos are
heavier and rarer than those of typical first galaxies, but are more likely to
end up in quasar hosts by $z\simeq 6$. This mechanism naturally yields a mass
ratio of $M_\bullet/M_\star >0.01$ higher than the value seen in the local
universe and the existence of such overmassive BHs provides us a unique
opportunity of detecting highly accreting seed BHs at $z\sim 15$ with AB
magnitude of $m_{\rm AB} \sim26 - 29$ mag at $2~\mu{\rm m}$ (rest-frame 10 eV)
by the upcoming observations by the James Webb Space Telescope and Nancy Grace
Roman Space Telescope.
