Recent ALMA observations of high-redshift normal galaxies have been providing a great opportunity to clarify the general origin of dust in the Universe , not biased to very bright special objects even at z > 6 . To clarify what constraint we can get for the dust enrichment in normal galaxies detected by ALMA , we use a theoretical model that includes major processes driving dust evolution in a galaxy ; that is , dust condensation in stellar ejecta , dust growth by the accretion of gas-phase metals , and supernova destruction . Using the dust emission fluxes detected in two normal galaxies at z > 6 by ALMA as a constraint , we can get the range of the time-scales ( or efficiencies ) of the above mentioned processes . We find that if we assume extremely high condensation efficiency in stellar ejecta ( f _ { \mathrm { in } } \ga 0.5 ) , rapid dust enrichment by stellar sources in the early phase may be enough to explain the observed ALMA flux , unless dust destruction by supernovae in those galaxies is stronger than that in nearby galaxies . If we assume a condensation efficiency expected from theoretical calculations ( f _ { \mathrm { in } } \la 0.1 ) , strong dust growth ( even stronger than assumed for nearby galaxies if they are metal-poor galaxies ) is required . These results indicate that the normal galaxies detected by ALMA at z > 6 are biased to objects ( i ) with high dust condensation efficiency in stellar ejecta , ( ii ) with strong dust growth in very dense molecular clouds , or ( iii ) with efficient dust growth because of fast metal enrichment up to solar metallicity . A measurement of metallicity is crucial to distinguish among these possibilities .