Some physics scenarios beyond the Standard Model of particle physics restore right-handed weak currents, which would manifest themselves in the polarization of the photon produced in $b\to s\gamma$ transitions. Due to the $V-A$ structure of the quark-$W$ coupling in the Standard Model, this polarization is strongly correlated with the flavour of the b-quark and suppresses interference responsible for time-dependent $CP$ violation in $B\to K_{res}\gamma$ decays. Observing sizable values of time-dependent asymmetries in these decays would therefore represent a null-test of the Standard Model. The Belle II experiment at the SuperKEKB energy-asymmetric $e^+ e^-$ collider is a substantial upgrade of the B factory facility at the Japanese KEK laboratory. The design luminosity of the machine is $8\times 10^{35}$ cm$^{-2}$s$^{-1}$ and the Belle II experiment aims to record 50 ab$^{-1}$ of data, a factor of 50 more than its predecessor. From February to July 2018, the machine has completed a commissioning run, achieved a peak luminosity of $5.5\times 10^{33}$ cm$^{-2}$s$^{-1}$, and Belle II has recorded a data sample of about 0.5 fb$^{-1}$. Main operation of SuperKEKB has started in March 2019. In this presentation we show how the final Belle II data set will allow to evaluate the time-dependent asymmetries for the final states $K_S^0\pi^0\gamma$ and $K_S^0\pi^+\pi^-\gamma with statistical uncertainties at the level of a few $10^{-2}$. As a preparatory exercise, we describe the first measurement of the B-lifetime with the early Belle II data, which already allows to understand accurate modelling of the time resolution as an essential ingredient.