  We present a determination of the magnitude of the Cabibbo-Kobayashi-Maskawa
(CKM) matrix element $V_{cb}$ using $B\to D\ell\nu$ decays. The result is based
on $e^+e^-\to\Upsilon(4S)$ data recorded by the Belle II detector corresponding
to 189.2/fb of integrated luminosity. The semileptonic decays $B^0\to D^-(\to
K^+\pi^-\pi^-)\ell^+\nu_\ell$ and $B^+\to\bar D^0(\to K^+\pi^-)\ell^+\nu_\ell$
are reconstructed, where $\ell$ is either electron or a muon. The second $B$
meson in the $\Upsilon(4S)$ event is not explicitly reconstructed. Using the
diamond-frame method, we determine the $B$ meson four-momentum and thus the
hadronic recoil. We extract the partial decay rates as functions of $w$ and
perform a fit to the decay form-factor and the CKM parameter $|V_{cb}|$ using
the BGL parameterization of the form factor and lattice QCD input from the
FNAL/MILC and HPQCD collaborations. We obtain $\eta_{EW}|V_{cb}|=(38.53\pm
1.15)\times 10^{-3}$, where $\eta_{EW}$ is an electroweak correction, and the
error accounts for theoretical and experimental sources of uncertainty.
