Typically the model requires anywhere between 6-12 hours to fully spin up. It will depend on the grid distances and time steps. The finer the grid size, the more time steps you would have in a given time window, hence faster spin-up. You may calculate the kinetic energy spectra at various model times to see how the model spins up (see Skamarock, W. C., 2004: Evaluating mesoscale NWP models using kinetic energy spectra. Mon. Wea. Rev., 132, 3019-3032). You may also compute d(surface pressure)/dt to see how the values settle down in time by turning on the option diag_print. One way to shorten the spin up time is to use digital filter initialization.
Spin-up time
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