<p>We present an efficient first-principles approach for simulating the nonequilibrium electron dynamic in extended systems beyond the linear regime. The method combines Koopmans-compliant functionals, which provide an accurate description of quasiparticle band structures, with the real-time evolution of the electronic density matrix in a Wannier basis within the Hartree plus screened exchange (HSEX) approximation. The locality of the orbital basis enables physically justified approximations that significantly reduce the computational and memory scaling of the method while preserving accuracy. We benchmark the approach in the linear regime against experimental spectra and reference GW-BSE calculations for systems featuring both weakly and strongly bound excitons. Moving to the nonlinear regime, we investigate high-harmonic generation (HHG) in silicon and lithium fluoride. While in silicon the HHG spectrum is largely governed by the quasi-particle band structure, we find that in materials featuring strong excitonic effect such as LiF the harmonic emission is selectively enhanced at excitonic resonances, suggesting that HHG probes correlated electron-hole excitations rather than solely the quasiparticle band structure. The present framework enables fully ab initio simulations of excitonic effects in nonlinear optical spectra at a significantly reduced computational cost compared to real-time many-body approaches, providing an efficient route to the study of ultrafast and strong-field phenomena in solids.</p> <p> </p>