Phototrophic organisms such as plants, photosynthetic bacteria, and algae use microscopic complexes of pigment molecules to absorb sunlight. Within the light-harvesting complexes, which frequently have several functional and structural subunits, the energy is transferred in the form of molecular excitations with very high efficiency. Green sulfur bacteria are considered to be among the most efficient light-harvesting organisms. Despite multiple experimental and theoretical studies of these bacteria, the physical origin of the efficient and robust energy transfer in their light-harvesting complexes is not well understood. To study excitation dynamics at the systems level, we introduce an atomistic model that mimics a complete light-harvesting apparatus of green sulfur bacteria. The model contains approximately 4000 pigment molecules and comprises a double wall roll for the chlorosome, a baseplate, and six Fenna-Matthews-Olson trimer complexes. We show that the fast relaxation within functional subunits combined with the transfer between collective excited states of pigments can result in robust energy funneling to the initial excitation conditions and temperature changes. Moreover, the same mechanism describes the coexistence of multiple time scales of excitation dynamics frequently observed in ultrafast optical experiments. While our findings support the hypothesis of supertransfer, the model reveals energy transport through multiple channels on different length scales.