  We show that Schwarzschild black hole binaries can undergo dynamical
scalarization (DS) in the inspiral phase, in a subclass of
$\mathbb{Z}_2$-symmetric Einstein-scalar-Gauss-Bonnet (ESGB) theories of
gravity. The mechanism is analogous to neutron star DS in scalar-tensor
gravity, and it differs from the late merger and ringdown black hole
(de)scalarization found in recent ESGB studies. To our knowledge, the new
parameter space we highlight was unexplored in numerical relativity
simulations. We also estimate the orbital separation at the DS onset, and
characterize the subsequent scalar hair growth at the adiabatic approximation.
