Observing signatures of light-induced topological Floquet states in materials has been shown to be very challenging. Angle-resolved photoemission spectroscopy (ARPES) is well suited for the investigation of Floquet physics, as it allows to directly probe the dressed electronic states of driven solids. Depending on the system, scattering and decoherence can play an important role, hampering the emergence of Floquet states. Another challenge is to disentangle Floquet side bands from laser-assisted photoemission (LAPE), since both lead to similar signatures in ARPES spectra. Here, we investigate the emergence of Floquet state in the transition metal dichalcogenide 2H-WSe₂, one of the most promising systems for observing Floquet physics. We discuss how the topological Floquet state manifests in characteristic features in the circular dichroism in photoelectron angular distributions (CDAD) that is determined by the transient band structure modifications and the associated texture of the orbital angular momentum. Combining highly accurate modeling of the photoemission matrix elements with an ab initio description of the light-matter interaction, we investigate regimes which can be realized in current state-of-the-art experimental setups. The predicted features are robust against scattering effects and are expected to be observed in forthcoming experiments.