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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$^{-1}$ ofcollision events recorded by the Belle II experiment at the SuperKEKBasymmetric-energy $e^+ e^-$ collider. For the $B^-\to D^{0}\ell^-\bar\nu_\ell$channel, we present first studies that isolate this decay from othersemileptonic processes and backgrounds. We report a measurement of the$\bar{B}^0 \to D^{*+} \ell^{-} \bar{\nu}_l$ branching fraction and obtain${\cal B}(\bar{B}^0 \to D^{*+} \ell^{-} \bar{\nu}_l) = \left(4.60 \pm0.05_{\mathrm{stat}}\pm0.17_{\mathrm{syst}} \pm 0.45_{\pi_s}\right) \%$, inagreement with the world average. Here, the uncertainties are statistical,systematic, and related to slow pion reconstruction, respectively. Thesystematic uncertainties are limited by the statistics of auxiliarymeasurements and will improve in the future. We also report differentialbranching fractions in five bins of the hadronic recoil parameter $w$ for$\bar{B}^0 \to D^{*+} \ell^{-} \bar{\nu}_l$, unfolded to account for resolutionand efficiency effects.

Studies of the semileptonic $\bar B^0\to D^{*+}\ell^-\bar\nu_\ell$ and  $B^-\to D^{0}\ell^-\bar\nu_\ell$ decay processes with 34.6 fb$^{-1}$ of Belle  II data