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ABSTRACT We study the formation of the TRAPPIST-1 (T1) planets starting shortly after Moon-sized bodies form just exterior to the ice line. Our model includes mass growth from pebble accretion and mergers, fragmentation, type-I migration, and eccentricity and inclination dampening from gas drag. We follow the composition evolution of the planets fed by a dust condensation code that tracks how various dust species condense out of the disc as it cools. We use the final planet compositions to calculate the resulting radii of the planets using a new planet interior structure code and explore various interior structure models. Our model reproduces the broader architecture of the T1 system and constrains the initial water mass fraction of the early embryos and the final relative abundances of the major refractory elements. We find that the inner two planets likely experienced giant impacts and fragments from collisions between planetary embryos often seed the small planets that subsequently grow through pebble accretion. Using our composition constraints, we find solutions for a two-layer model, a planet comprised of only a core and mantle, that match observed bulk densities for the two inner planets b and c. This, along with the high number of giant impacts the inner planets experienced, is consistent with recent observations that these planets are likely desiccated. However, two-layer models seem unlikely for most of the remaining outer planets, which suggests that these planets have a primordial hydrosphere. Our composition constraints also indicate that no planets are consistent with a core-free interior structure.