Graphyne (GY) and graphdiyne (GDY)-based monolayers represent the next generation 2D carbon-rich materials with tunable structures and properties surpassing those of graphene. However, the detection of band formation in atomically thin GY/GDY analogues has been challenging, as both long-range order and atomic precision have to be fulfilled in the system. The present work reports direct evidence of band formation in on-surface synthesized metallated Ag-GDY sheets with mesoscopic (≈1 µm) regularity. Employing scanning tunneling and angle-resolved photoemission spectroscopies, energy-dependent transitions of real-space electronic states above the Fermi level and formation of the valence band are respectively observed. Furthermore, density functional theory (DFT) calculations corroborate the observations and reveal that doubly degenerate frontier molecular orbitals on a honeycomb lattice give rise to flat, Dirac and Kagome bands close to the Fermi level. DFT modeling also indicates an intrinsic band gap for the pristine sheet material, which is retained for a bilayer with h-BN, whereas adsorption-induced in-gap electronic states evolve at the synthesis platform with Ag-GDY decorating the (111) facet of silver. These results illustrate the tremendous potential for engineering novel band structures via molecular orbital and lattice symmetries in atomically precise 2D carbon materials.