  Mapping Cosmic Dawn with 21-cm tomography offers an exciting new window into
the era of primordial star formation. However, self-consistent implementation
of both the process of star formation and the related 21-cm signal is
challenging, due to the multi-scale nature of the problem. In this study, we
develop a flexible semi-analytical model to follow the formation of the first
stars and the process of gradual transition from primordial to metal-enriched
star formation. For this transition we use different in scenarios with varying
time-delays (or recovery times) between the first supernovae and the formation
of the second generation of stars. We use recovery times between 10 and
100\,Myr and find that these delays have a strong impact on the redshift at
which the transition to metal-enriched star formation occurs. We then explore
the effect of this transition on the 21-cm signal and find that the recovery
time has a distinctive imprint in the signal. Together with an improved
understanding of how this time-delay relates to the properties of
Population~III stars, future 21-cm observations can give independent
constraints on the earliest epoch of star formation.
