  We investigate the level of galaxy assembly bias in the Sloan Digital Sky
Survey (SDSS) main galaxy sample using ELUCID, a state-of-the-art constrained
simulation that accurately reconstructed the initial density perturbations
within the SDSS volume. On top of the ELUCID haloes, we develop an extended HOD
model that includes the assembly bias of central and satellite galaxies,
parameterized as $\mathcal{Q}_\mathrm{cen}$ and $\mathcal{Q}_\mathrm{sat}$,
respectively, to predict a suite of one- and two-point observables. In
particular, our fiducial constraint employs the probability distribution of the
galaxy number counts measured on $8\,\mathrm{Mpc}\,h^{-1}$ scales $N_8^g$ and
the projected cross-correlation functions of quintiles of galaxies selected by
$N_8^g$ with our entire galaxy sample. We perform extensive tests of the
efficacy of our method by fitting the same observables to mock data using both
constrained and non-constrained simulations. We discover that in many cases the
level of cosmic variance between the two simulations can produce biased
constraints that lead to an erroneous detection of galaxy assembly bias if the
non-constrained simulation is used. When applying our method to the SDSS data,
the ELUCID reconstruction effectively removes an otherwise strong degeneracy
between cosmic variance and galaxy assembly bias in SDSS, enabling us to derive
an accurate and stringent constraint on the latter. Our fiducial ELUCID
constraint, for galaxies above a stellar mass threshold
$M_*{=}10^{10.2}\,h^{-2}\,M_\odot$, is
$\mathcal{Q}_\mathrm{cen}{=}{-}0.09\pm{0.05}$ and
$\mathcal{Q}_\mathrm{sat}{=}0.09\pm{0.10}$, indicating no evidence for a
significant~($>2\sigma$) galaxy assembly bias in the local Universe probed by
SDSS. Finally, our method provides a promising path to the robust modelling of
the galaxy-halo connection within future surveys like DESI and PFS.
