We use numerical relativity to study the scalar field evolution sourced by hyperbolic encounters of black holes in quadratic scalar Gauss-Bonnet gravity. In this theory, single black holes are known to acquire a scalar hair through scalarization for certain values of their mass and spin. We work in the decoupling limit and evolve the scalar field on top of a background metric. Seeding binary black holes with an initial scalar field, we find that configurations which initially cannot sustain a scalar hair temporarily scalarize during an encounter and thereby exhibit dynamical scalarization. This is possible for both positive and negative couplings between the scalar field and curvature in black hole binaries with zero and non-zero initial spins, respectively. Furthermore, we find that the change in the spin magnitude of black holes during certain hyperbolic encounters can lead to permanent spin-induced scalarization (or descalarization), which we refer to as spin-up (de)scalarization.