  In this work, we use the constrained Gaussian realization technique to study
the early growth of supermassive black holes (SMBHs) in cosmological
hydrodynamic simulations, exploring its relationship with features of the
initial density peaks on large scales, ~1 Mpc/h. Our constrained simulations of
volume (20 Mpc/h)^3 successfully reconstruct the large-scale structure as well
as the black hole growth for the hosts of the rare 10^9 Msun SMBHs found in the
BlueTides simulation at z~7. We run a set of simulations with constrained
initial conditions by imposing a 5 \sigma_0(R_G) peak on scale of R_G = 1 Mpc/h
varying different peak features, such as the shape and compactness as well as
the tidal field surrounding the peak. We find that initial density peaks with
high compactness and low tidal field induce the most rapid BH growth at early
epochs. This is because compact density peaks with a more spherical large scale
matter distribution lead to the formation of high density gas clumps in the
centers of halos, and thus boost early BH accretion. Moreover, such initially
compact density peaks in low tidal field regions also lead to a more compact BH
host galaxy morphology. This can explain the tight correlation between BH
growth and host galaxy compactness seen in observations.
