  We report measurements of the $\bar{B}^0 \to D^{*+} \ell^{-} \bar{\nu}_l$ and
$B^- \to D^{0} \ell^{-} \bar{\nu}_l$ processes using 34.6 fb$^{-1}$ of
collision events recorded by the Belle II experiment at the SuperKEKB
asymmetric-energy $e^+ e^-$ collider. For the $B^-\to D^{0}\ell^-\bar\nu_\ell$
channel, we present first studies that isolate this decay from other
semileptonic processes and backgrounds. We report a measurement of the
$\bar{B}^0 \to D^{*+} \ell^{-} \bar{\nu}_l$ branching fraction and obtain
${\cal B}(\bar{B}^0 \to D^{*+} \ell^{-} \bar{\nu}_l) = \left(4.60 \pm
0.05_{\mathrm{stat}}\pm0.17_{\mathrm{syst}} \pm 0.45_{\pi_s}\right) \%$, in
agreement with the world average. Here, the uncertainties are statistical,
systematic, and related to slow pion reconstruction, respectively. The
systematic uncertainties are limited by the statistics of auxiliary
measurements and will improve in the future. We also report differential
branching fractions in five bins of the hadronic recoil parameter $w$ for
$\bar{B}^0 \to D^{*+} \ell^{-} \bar{\nu}_l$, unfolded to account for resolution
and efficiency effects.
