Subcomponent millicharged dark matter that cools baryons via Coulomb interactions has been invoked to explain the EDGES anomaly. However, this model is in severe tension with constraints from cosmology and stellar emissions. In this work, we consider the consequences of these millicharged particles existing in composite Q-balls. The relevant degrees of freedom at high temperature are minuscule elementary charges, which fuse at low temperatures to make up Q-balls of larger charge. These Q-balls serve as the degrees of freedom relevant in cooling the baryons sufficiently to account for the EDGES anomaly. In such a model, cosmology and stellar constraints (which involve high-temperature processes) apply only to the feebly interacting elementary charges and not to the Q-balls. This salvages a large range of parameter space for millicharged Q-balls that can explain the EDGES anomaly. It also opens up new parameter space for direct detection, albeit at low momentum transfers.