We use cosmological hydrodynamic zoom-in simulations to study early structure formation in two dark matter (DM) cosmologies, the standard CDM model, and a thermal warm DM (WDM) model with a particle mass of m χ c 2 = 3 keV. We focus on DM haloes with virial masses M ∼ 10 10 M . We find that the first star formation activity is delayed by ∼ 200 Myr in the WDM model, with similar delays for metal enrichment and the formation of the second generation of stars. However, the differences between the two models in globally-averaged properties, such as star formation rate density and mean metallicity, decrease towards lower redshifts (z 10). Metal enrichment in the WDM cosmology is restricted to dense environments, while low-density gas can also be significantly enriched in the CDM case. The free-free contribution from early structure formation at redshifts z > 6 to the cosmic radio background (CRB) is 3 +13 −1.5 % (8 +33 −3.5 %) of the total signal inferred from radio experiments such as ARCADE 2, in the WDM (CDM) model. The direct detection of the H 2 emission from early structure formation (z 7.2), originating from the low-mass haloes explored here, will be challenging even with the next generation of far-infrared space telescopes, unless the signal is magnified by at least a factor of 10 via gravitational lensing or shocks. However, more massive haloes with M 10 12 M may be observable for z 10, even without magnification, provided that our extrapolation from the scale of our simulated haloes is valid.