Globular protein hydrogels are an emerging class of materials with the potential for rational design, and a generalized understanding of how their network properties emerge from the structure and dynamics of the building block is a key challenge. Here we computationally investigate the effect of intermediate (polymeric) nanoscale structure on the formation of protein hydrogels. We show that changes in both the cross-link topology and flexibility of the polymeric building block lead to changes in the force transmission around the system and provide insight into the dynamic network formation processes. The preassembled intermediate structure provides a novel structural coordinate for the hierarchical modulation of macroscopic network properties, as well as furthering our understanding of the general dynamics of network formation.