Recent observations suggest that disks around type II protostars do not contain enough dust to account for the observed exoplanet population. Younger disks appear to be more massive, hinting towards the onset of planet formation in the earliest stages of star formation and the rapid assembly of planetary cores. We investigate planet formation through pebble accretion in young disks and discuss the outcome in terms of the observed dust disk mass distribution around class 0 protostars. We find that giant planet formation is possible only within the 30% most massive disks. Giant planets can form at large orbital distances (>10 au) but should be rare, in qualitative agreement with observational inferences.