  Non-linear structure formation for fermionic dark matter particles leads to
dark matter density profiles with a degenerate compact core surrounded by a
diluted halo. For a given fermion mass, the core has a critical mass that
collapses into a supermassive black hole (SMBH). Galactic dynamics constraints
suggest a $\sim 100$ keV/$c^2$ fermion, which leads to $\sim 10^7 M_\odot$
critical core mass. Here, we show that baryonic (ordinary) matter accretion
drives an initially stable dark matter core to SMBH formation and determine the
accreted mass threshold that induces it. Baryonic gas density $\rho_b$ and
velocity $v_b$ inferred from cosmological hydro-simulations and observations
produce sub-Eddington accretion rates triggering the baryon-induced collapse in
less than a Gyr. This process produces active galactic nuclei in galaxy mergers
and the high-redshift Universe. For TXS 2116-077, merging with a nearby galaxy,
the observed $3\times 10^7 M_\odot$ SMBH, for $Q_b = \rho_b/v_b^3 = 0.125
M_\odot/(100 \text{km/s pc})^3$, forms in $\approx 0.6$ Gyr, consistent with
the $0.5$-$2$ Gyr merger timescale and younger jet. For the farthest central
SMBH detected by the \textit{Chandra} X-ray satellite in the $z=10.3$ UHZ1
galaxy observed by the James Webb Space Telescope (\textit{JWST}), the
mechanism leads to a $4\times 10^7 M_\odot$ SMBH in $87$-$187$ Myr, starting
the accretion at $z=12$-$15$. The baryon-induced collapse can also explain the
$\approx 10^7$-$10^8 M_\odot$ SMBHs revealed by the JWST at $z\approx 4$-$6$.
After its formation, the SMBH can grow to a few $10^9 M_\odot$ in timescales
shorter than a Gyr via sub-Eddington baryonic mass accretion.
