  Models of planetary core growth by either planetesimal or pebble accretion
are traditionally disconnected from the models of dust evolution and formation
of the first gravitationally-bound planetesimals. The state-of-the-art models
typically start with massive planetary cores already present. We aim to study
the formation and growth of planetary cores in a pressure bump, motivated by
the annular structures observed in protoplanetary disks, starting with
sub-micron-sized dust grains. We connect the models of dust coagulation and
drift, planetesimal formation in the streaming instability, gravitational
interactions between planetesimals, pebble accretion, and planet migration,
into one uniform framework. We find that planetesimals forming early at the
massive end of the size distribution grow quickly dominantly by pebble
accretion. These few massive bodies grow on the timescales of ~100 000 years
and stir the planetesimals formed later preventing the emergence of further
planetary cores. Additionally, a migration trap occurs allowing for retention
of the growing cores. Pressure bumps are favourable locations for the emergence
and rapid growth of planetary cores by pebble accretion as the dust density and
grain size are increased and the pebble accretion onset mass is reduced
compared to a smooth-disk model.
