ABSTRACT The Solar system gas giants are each surrounded by many moons, with at least 50 prograde satellites thought to have formed from circumplanetary material. Just like the Sun is not the only star surrounded by planets, extrasolar gas giants are likely surrounded by satellite systems. Here, we report on Atacama Large Millimeter/Submillimeter Array (ALMA) observations of four <40 Myr old stars with directly imaged companions: PZ Tel, AB Pic, 51 Eri, and κ And. Continuum emission at 1.3 mm is undetected for any of the systems. Since these are directly imaged companions, there is knowledge of their temperatures, masses, and locations. These allow for upper limits on the amount of circumplanetary dust to be derived from detailed radiative transfer models. These protolunar disc models consider two disc sizes: 0.4 and 0.04 times the exoplanet’s Hill radius. The former is representative of hydrodynamic simulations of circumplanetary discs, while the latter a case with significant radial drift of solids. The more compact case is also motivated by the semimajor axis of Callisto, enclosing Jupiter’s Galilean satellites. All upper limits fall below the expected amount of dust required to explain regular satellite systems (∼10−4 times the mass of their central planet). Upper limits are compared with viscous evolution and debris disc models. Our analysis suggests that the non-detections can be interpreted as evidence of dust growth beyond metre sizes to form moonetesimals in time-scales ≲10 Myr. This sample increases by 50 per cent the number of ALMA non-detections of young companions available in the literature.