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Supersonic relative motion between baryons and dark matter due to the decoupling of baryons from the primordial plasma after recombination affects the growth of the first small-scale structures. Large box sizes (greater than a few hundred Mpc) are required to sample the full range of scales pertinent to the relative velocity, while the effect of the relative velocity is strongest on small scales (less than a few hundred kpc). This separation of scales naturally lends itself to the use of `zoom' simulations, and here we present our methodology to self-consistently incorporate the relative velocity in zoom simulations, including its cumulative effect from recombination through to the start time of the simulation. We apply our methodology to a large-scale cosmological zoom simulation, finding that the inclusion of relative velocities suppresses the halo baryon fraction by $46$--$23$ per cent between $z=13.6$ and $11.2$, in qualitative agreement with previous works. In addition, we find that including the relative velocity delays the formation of star particles by $\sim 20 {~\rm Myr}$ Myr on average (of the order of the lifetime of a $\sim 9~{\rm M}_\odot$ Population III star) and suppresses the final stellar mass by as much as $79$ per cent at $z=11.2$.