The ionization rate of an atom in a strong optical field can be resonantly enhanced by the presence of long-living atomic levels (so-called Freeman resonances). This process is most prominent in the multiphoton ionization regime, meaning that the ionization event takes many optical cycles. Nevertheless, here, we show that these resonances can lead to rapid subcycle-scale plasma buildup at the resonant values of the intensity in the pump pulse. The fast buildup can break the cycle-to-cycle symmetry of the ionization process, resulting in the generation of persistent macroscopic plasma currents which remain after the end of the pulse. This, in turn, gives rise to a broadband radiation of unusual spectral structure, forming a comb from terahertz to visible. This radiation contains fingerprints of the attosecond electron dynamics in Rydberg states during ionization. © 2017 American Physical Society.