Observational searches for faint active nuclei at z > 6 have been extremely elusive, with a few candidates whose high-z nature is still to be confirmed. Interpreting this lack of detections is crucial to improve our understanding of high-z supermassive black holes (SMBHs) formation and growth. In this work, we present a model for the emission of accreting BHs in the X-ray band, taking into account super-Eddington accretion, which can be very common in gas-rich systems at high-z. We compute the spectral energy distribution for a sample of active galaxies simulated in a cosmological context, which represent the progenitors of a z ∼ 6 SMBH with M BH ∼ 10 9 M . We find an average Compton thick fraction of ∼ 45% and large typical column densities (N H 10 23 cm 2 ). However, faint progenitors are still luminous enough to be detected in the X-ray band of current surveys. Even accounting for a maximum obscuration effect, the number of detectable BHs is reduced at most by a factor 2. In our simulated sample, observations of faint quasars are mainly limited by their very low active fraction ( f act ∼ 1%), which is the result of short, super-critical growth episodes. We suggest that to detect high-z SMBHs progenitors, large area surveys with shallower sensitivities, such as Cosmos Legacy and XMM-LSS+XXL, are to be preferred with respect to deep surveys probing smaller fields, such as CDF-S. 1 Hereafter we adopt a Lambda Cold Dark Matter (ΛCDM) cosmology with parameters Ω M = 0.314, Ω Λ = 0.686, and h = 0.674 (Planck Collaboration et al. 2014).