  We report on a LUCI/Large Binocular Telescope near-infrared (NIR) spectrum of
PSO J030947.49+271757.31 (hereafter PSO J0309+27), the highest redshift blazar
known to date (z$\sim$6.1). From the C$\rm IV$$\lambda$1549 broad emission line
we found that PSO J0309+27 is powered by a
1.45$^{+1.89}_{-0.85}$$\times$10$^9$M$_{\odot}$ supermassive black hole (SMBH)
with a bolometric luminosity of $\sim$8$\times$10$^{46}$ erg s$^{-1}$ and an
Eddington ratio equal to 0.44$^{+0.78}_{-0.35}$. We also obtained new
photometric observations with the Telescopio Nazionale Galileo in J and K bands
to better constrain the NIR Spectral Energy Distribution of the source. Thanks
to these observations, we were able to model the accretion disk and to derive
an independent estimate of the black hole mass of PSO J0309+27, confirming the
value inferred from the virial technique. The existence of such a massive SMBH
just $\sim$900 million years after the Big Bang challenges models of the
earliest SMBH growth, especially if jetted Active Galactic Nuclei are
associated to a highly spinning black hole as currently thought. Indeed, in a
Eddington-limited accretion scenario and assuming a radiative efficiency of
0.3, typical of a fast rotating SMBH, a seed black hole of more than 10$^6$
M$_{\odot}$ at z = 30 is required to reproduce the mass of PSO J0309+27 at
redshift 6. This requirement suggests either earlier periods of rapid black
hole growth with super-Eddington accretion and/or that only part of the
released gravitational energy goes to heat the accretion disk and feed the
black hole.
