Planet formation models begin with proto-embryos and planetesimals already fully formed, missing out a crucial step, the formation of planetesimals/proto-embryos. In this work, we include prescriptions for planetesimal and proto-embryo formation arising from pebbles becoming trapped in short-lived pressure bumps, in thermally evolving viscous discs to examine the sizes and distributions of proto-embryos and planetesimals throughout the disc. We find that planetesimal sizes increase with orbital distance, from ~10 km close to the star to hundreds of kilometres further away. Proto-embryo masses are also found to increase with orbital radius, ranging from $10^{-6} M_{rm oplus}$ around the iceline, to $10^{-3} M_{rm oplus}$ near the orbit of Pluto. We include prescriptions for pebble and planetesimal accretion to examine the masses that proto-embryos can attain. Close to the star, planetesimal accretion is efficient due to small planetesimals, whilst pebble accretion is efficient where pebble sizes are fragmentation limited, but inefficient when drift dominated due to low accretion rates before the pebble supply diminishes. Exterior to the iceline, planetesimal accretion becomes inefficient due to increasing planetesimal eccentricities, whilst pebble accretion becomes more efficient as the initial proto-embryo masses increase, allowing them to significantly grow before the pebble supply is depleted. Combining both scenarios allows for more massive proto-embryos at larger distances, since the accretion of planetesimals allows pebble accretion to become more efficient, allowing giant planet cores to form at distances upto 10 au. By including more realistic initial proto-embryo and planetesimal sizes, as well as combined accretion scenarios, should allow for a more complete understanding in the beginning to end process of how planets and planetary systems form.
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