Core-collapse supernovae ( SNe ) are believed to be the first significant source of dust in the Universe . Such SNe are expected to be the main dust producers in young high-redshift Lyman \alpha emitters ( LAEs ) given their young ages , providing an excellent testbed of SN dust formation models during the early stages of galaxy evolution . We focus on the dust enrichment of a specific , luminous LAE ( Himiko , z \simeq 6.6 ) for which a stringent upper limit of 52.1 ~ { } \mu Jy ( 3 \sigma ) has recently been obtained from ALMA continuum observations at 1.2 mm . We predict its submillimetre dust emission using detailed models that follow SN dust enrichment and destruction and the equilibrium dust temperature , and obtain a plausible upper limit to the dust mass produced by a single SN : m _ { \mathrm { d,SN } } < 0.15 – 0.45 ~ { } \mathrm { M } _ { \sun } , depending on the adopted dust optical properties . These upper limits are smaller than the dust mass deduced for SN 1987A and that predicted by dust condensation theories , implying that dust produced in SNe are likely to be subject to reverse shock destruction before being injected into the interstellar medium . Finally , we provide a recipe for deriving m _ { \mathrm { d,SN } } from submillimetre observations of young , metal poor objects wherein condensation in SN ejecta is the dominant dust formation channel .