  The repointing time of the XRT instrument on the Neil Gehrels Swift
Observatory satellite has posed challenges in observing and studying the early
X-ray emissions within $\approx40$ s after a gamma-ray burst (GRB) trigger. To
address this issue, we adopt a novel approach that capitalizes on the
cosmological time dilation in GRBs with redshifts ranging from $3$ to $9$.
Applying this strategy to Swift/XRT data, we investigate the earliest X-ray
emissions of $368$ GRBs from the Swift catalog, including short and long GRBs.
We compare the time delay between the GRB trigger and the initial Swift/XRT
observation, measured in the GRB observer frame (OTD) and the cosmological
rest-frame (RTD). This technique is here used in the analysis of GRB 090423 at
$z=8.233$ (RTD $\sim8.2$ s), GRB 090429B at $z\approx9.4$ (RTD $\sim10.1$ s),
and GRB 220101A at $z=4.61$ (RTD $\sim14.4$ s). The cosmological time dilation
enables us to observe the very early X-ray afterglow emission in these three
GRBs. We thus validate the observation of the collapse of the carbon-oxygen
(CO) core and the coeval newborn neutron star ($\nu$NS) formation triggering
the GRB event in the binary-driven hypernova (BdHN) scenario. We also evidence
the $\nu$NS spin-up due to supernova ejecta fallback and its subsequent slowing
down due to the X-optical-radio synchrotron afterglow emission. A brief
gravitational wave signal may separate the two stages due to a fast-spinning
$\nu$NS triaxial-to-axisymmetric transition. We also analyze the long GRB
redshift distribution for the different BdHN types and infer that BdHNe II and
III may originate the NS binary progenitors of short GRBs.
