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For several decades, astronomers have measured the electromagnetic emission in the universe from the lowest to the highest energies with incredible precision. The lowest end of the spectrum, corresponding to radio waves, is fairly well studied and understood. Yet there is a long standing discrepancy between measurements and predictions, which has prompted the construction of many new models of radio emitters. Here we show that remnant electron-proton interactions, leading to photon production in the early universe, also referred to as cosmic free-free emission, solves the discrepancy between theory and observations. While the possibility of cosmic free-free emission has been postulated for several decades, this is the first time that the amplitude and shape of the signal has been computed and its existence demonstrated. Using current measurements we estimate this emission to become important from around a redshift of $z \simeq 2150$. This contribution from fundamental particles and interactions represents the lowest energy test from the early universe of one of the pillars of modern physics, Quantum Electrodynamics. The next generation of deep radio surveys will be able to measure primordial signals from this cosmic era with greater precision and further solidify our understanding of the radio sky.