Topological insulators are classified according to their symmetries. Discovery of them in electronic solids is thus restricted by orbital and crystalline symmetries available in nature. Synthetic quantum matter, such as the recent double-well optical lattices loaded with s and p orbital ultracold atoms, can exploit symmetries and interaction beyond natural conditions. Here we unveil a topological phase of interacting fermionic atoms on a two-leg ladder derived from the above experimental optical lattice by dimension reduction. The topological band structure originates from the staggered phases of sp orbital tunnelling, requiring neither spin-orbit coupling nor other known mechanisms like p-wave pairing, artificial gauge field or rotation. Upon crossing over to two-dimensional coupled ladders, the edge modes from individual ladder form a parity-protected flat band at zero energy. Experimental signatures are found in density correlations and phase transitions to trivial band and Mott insulators.