G0.253+0.016, aka 'the Brick', is one of the most massive (>10(5) M-circle dot) and dense (>10(4) cm(-3)) molecular clouds in the Milky Way's Central Molecular Zone. Previous observations have detected tentative signs of active star formation, most notably a water maser that is associated with a dust continuum source. We present ALMA Band 6 observations with an angular resolution of 0.13 arcsec (1000 AU) towards this 'maser core' and report unambiguous evidence of active star formation within G0.253+0.016. We detect a population of eighteen continuum sources (median mass similar to 2 M-circle dot), nine of which are driving bi-polar molecular outflows as seen via SiO (5-4) emission. At the location of the water maser, we find evidence for a protostellar binary/multiple with multidirectional outflow emission. Despite the high density of G0.253+0.016, we find no evidence for high-mass protostars in our ALMA field. The observed sources are instead consistent with a cluster of low-to-intermediate-mass protostars. However, the measured outflow properties are consistent with those expected for intermediate-to-high-mass star formation. We conclude that the sources are young and rapidly accreting, and may potentially form intermediate- and high-mass stars in the future. The masses and projected spatial distribution of the cores are generally consistent with thermal fragmentation, suggesting that the large-scale turbulence and strong magnetic field in the cloud do not dominate on these scales, and that star formation on the scale of individual protostars is similar to that in Galactic disc environments.