We study, by means of dedicated simulations of massive black hole build-up, the possibility to constraint the existence and nature of the active galactic nucleus (AGN) population at z≳ 6 with available and planned X-ray and near-infrared space telescopes. We find that X-ray deep field observations can set important constraints to the faint-end of the AGN luminosity function at very high redshift. Planned X-ray telescopes should be able to detect AGN hosting black holes with masses down to ≳105 M⊙ (i.e. X-ray luminosities in excess of 1042 erg s−1), and can constrain the evolution of the population of massive black hole at early times (6 ≲z≲ 10). We find that this population of AGN should contribute substantially (∼25 per cent) to the unresolved fraction of the cosmic X-ray background in the 0.5–10 keV range, and that a significant fraction (∼3–4 per cent) of the total background intensity would remain unaccounted even after future X-ray observations. As byproduct, we compute the expected ultraviolet background from AGN at z≳ 6, and we discuss the possible role of AGN in the reionization of the Universe at these early epochs, showing that AGN alone can provide enough ionizing photons only in the (improbable) case of an almost completely homogeneous intergalactic medium. Finally, we show that super-Eddington accretion, suggested by the observed quasi-stellar objects at z≃ 6, must be a very rare event, confined to black holes living in the highest density peaks.