Our current knowledge of star formation and accretion luminosity at high redshift (z > 3–4), as well as the possible connections between them, relies mostly on observations in the rest-frame ultraviolet, which are strongly affected by dust obscuration. Due to the lack of sensitivity of past and current infrared instrumentation, so far it has not been possible to get a glimpse into the early phases of the dust-obscured Universe. Among the next generation of infrared observatories, SPICA, observing in the 12–350 µm range, will be the only facility that can enable us to trace the evolution of the obscured star-formation rate and black-hole accretion rate densities over cosmic time, from the peak of their activity back to the reionisation epoch (i.e., 3 < z ≲ 6–7), where its predecessors had severe limitations. Here, we discuss the potential of photometric surveys performed with the SPICA mid-infrared instrument, enabled by the very low level of impact of dust obscuration in a band centred at 34 µm. These unique unbiased photometric surveys that SPICA will perform will fully characterise the evolution of AGNs and star-forming galaxies after reionisation.