Two distinct scenarios for the origin of the ~4 × 10 8 M sun of dust observed in the high-redshift (z = 6.4) quasar J1148+5251 have been proposed. The first assumes that this galaxy is much younger than the age of the universe at that epoch so that only supernovae (SNe) could have produced this dust. The second scenario assumes a significantly older galactic age, so that the dust could have formed in lower-mass asymptotic giant branch (AGB) stars. Presenting new integral solutions for the chemical evolution of metals and dust in galaxies, we offer a critical evaluation of these two scenarios and observational consequences that can discriminate between the two. We show that AGB stars can produce the inferred mass of dust in this object, howe...