Phases of matter with nontrivial topological order are predicted to exhibit a variety of exotic phenomena, such as robust localized bound states in 1D systems, and edge states in 2D systems, which are expected to display spin helicity, immunity to backscattering, and weak antilocalization. In this Letter, we present an experimental observation of topological structures generated via the controlled implementation of two consecutive noncommuting rotations in photonic discrete-time quantum walks. The second rotation introduces valleylike Dirac points in the system, allowing us to create the nontrivial topological pattern. By choosing specific values for the rotations, it is possible to coherently drive the system between topological sectors characterized by different topological invariants. We probe the full topological landscape, demonstrating the emergence of localized bound states hosted at the topological boundaries, and the existence of extremely localized or delocalized non-Gaussian quantum states. Our results pave the way for the study of valley polarization and applications of topological mechanisms in robust optical-device engineering.