Isolated chaotic many-body quantum systems can reach thermal equilibrium, but it is not yet clear
how long they take to do so. To answer this question, we use exact numerical methods and analyze
the entire evolution, from perturbation to thermalization, of a paradigmatic disordered many-body
quantum system in the chaotic regime. We investigate how the thermalization time depends on the
system size and observables. We show that if dynamical manifestations of spectral correlations in
the form of the correlation hole ("ramp") are taken into account, the time for thermalization scales
exponentially with system size, while if they are neglected, the scaling is better described by a power
law with system size, though with an exponent larger than expected for diffusive transport.