The nonlinear Hall effect has attracted much attention due to the famous, widely adopted interpretation in terms of the Berry curvature dipole in momentum space. Using ab initio Boltzmann transport equations, we find a 60% enhancement in the nonlinear Hall effect of n-doped GeTe and its noticeable frequency dependence, qualitatively different from the predictions based on the Berry curvature dipole. The origin of these differences is long-lived valley polarization in the electron distribution arising from electron-phonon scattering. Our findings await immediate experimental confirmation.