Axion quark nuggets (AQN) are hypothetical, macroscopically large objects with a mass greater than a few grams and sub-micrometer size, formed during the quark-hadrontransition. Originating from the axion field, they offer a possible resolution of the similarity between visible and dark components of the Universe, i.e. ΩDM ∼ Ωvisible and observed matter-antimatter asymmetry. These composite objects behave as cold dark matter, interacting with ordinary matter and resulting in pervasive electromagnetic radiation throughout the Universe. This work aims to predict the electromagnetic signature in large-scale structures from this AQN-baryon interaction, accounting for thermal and non-thermal radiations.We use Magneticum hydrodynamical simulations to describe the realistic distribution and dynamics of gas and dark matter at cosmological scales. We construct a light cone encompassing a 1.4 square degree area on the sky, extending up to redshift z = 5.4, and we calculate the electromagnetic signature across a wide range of frequencies from radio, starting at ν ∼ 1 GHz, up to a few keV X-ray energies. We find that the AQNs electromagnetic signature is characterized by global (monopole) and fluctuation signals. The amplitude of both signals strongly depends on the average nugget mass and the ionization level of the baryonic environment, allowing us to identify a most optimistic scenario and a minimal configuration. The signal of our most optimistic scenario is often near the sensitivity limit of existing instruments, such as FIRAS in the ν = [100-500] GHz range and the South Pole Telescope for high-resolution ℓ > 4000 at ν = 95 GHz. Fluctuations in the Extra-galactic Background Light caused by the axion quark nuggets in the most optimistic scenario can also be tested with space-based imagers Euclid and James Webb Space Telescope. In general, our minimal configuration is still out of reach of existing instruments, but future experiments might be able to pose some constraints.We conclude that the axion quark nuggets model represents a viable model for dark matter, which does not violate the canons of cosmology nor existing observations. A reanalysis of existing data sets could provide some evidence of axion quark nuggets if our most optimistic configuration is correct. The best chances for testing the model reside in 1) ultra-deep infrared and optical surveys, 2) future experiments to probe the frequency spectrum of the cosmic microwave background, and 3) low-frequency (1 GHz < ν < 100 GHz) and high-resolution (ℓ ≳ 104) observations.