Context : Aims : The aim is to elucidate the astrophysical conditions required for generating large amounts of dust in massive starburst galaxies at high redshift . Methods : We have developed a numerical galactic chemical evolution model . The model is constructed such that the effect of a wide range of parameters can be investigated . It takes into account results from stellar evolution models , a differentiation between diverse types of core collapse supernovae ( CCSN ) , and the contribution of asymptotic giant branch ( AGB ) stars in the mass range 3–8 \mathrm { M } _ { \odot } . We consider the lifetime-dependent yield injection into the interstellar medium ( ISM ) by all sources , and dust destruction due to supernova ( SN ) shocks in the ISM . We ascertain the temporal progression of the dust mass and the dust-to-gas and dust-to-metal mass ratios , as well as other physical properties of a galaxy , and study their dependence on the mass of the galaxy , the initial mass function ( IMF ) , dust production efficiencies , and dust destruction in the ISM . Results : The amount of dust and the physical properties of a galaxy strongly depend on the initial gas mass available . Overall , while the total amount of dust produced increases with galaxy mass , the detailed outcome depends on the SN dust production efficiency , the IMF , and the strength of dust destruction in the ISM . Dust masses are higher for IMFs biased towards higher stellar masses , even though these IMFs are more strongly affected by dust destruction in the ISM . The sensitivity to the IMF increases as the mass of the galaxy decreases . SNe are primarily responsible for a significant enrichment with dust at early epochs ( < 200 Myr ) . Dust production with a dominant contribution by AGB stars is found to be insufficient to account for dust masses in excess of 10 ^ { 8 } \mathrm { M } _ { \odot } within 400 Myr after starburst . Conclusions : We find that galaxies with initial gas masses between 1–5 \times 10 ^ { 11 } \mathrm { M } _ { \odot } are massive enough to enable production of dust masses > 10 ^ { 8 } \mathrm { M } _ { \odot } . Our preferred scenario is dominated by SN dust production in combination with top-heavy IMFs and moderate dust destruction in the ISM .