We present a picosecond time-resolved X-ray absorption spectroscopy (tr-XAS) setup designed for synchrotron-based studies of interfacial photochemical dynamics. The apparatus combines a high power, variable repetition rate picosecond laser system with a time-resolved X-ray fluorescence yield detection technique. Time-tagging of the detected fluorescence signals enables the parallel acquisition of X-ray absorption spectra at a variety of pump-probe delays employing the well-defined time structure of the X-ray pulse trains. The viability of the setup is demonstrated by resolving dynamic changes in the fine structure near the O1s X-ray absorption edge of cuprous oxide (Cu2O) after photo-excitation with a 355 nm laser pulse. Two distinct responses are detected. A pronounced, quasi-static, reversible change of the Cu2O O1s X-ray absorption spectrum by up to ∼30% compared to its static line shape corresponds to a redshift of the absorption edge by ∼1 eV. This value is small compared to the 2.2 eV band gap of Cu2O but in agreement with previously published results. The lifetime of this effect exceeds the laser pulse-to-pulse period of 8 μs, resulting in a quasi-static spectral change that persists as long as the sample is exposed to the laser light, and completely vanishes once the laser is blocked. Additionally, a short-lived response corresponding to a laser-induced shift of the main absorption line by ∼2 eV to lower energies appears within <200 ps and decays with a characteristic timescale of 43 ± 5 ns. Both the picosecond rise and nanosecond decay of this X-ray response are simultaneously captured by making use of a time-tagging approach - highlighting the prospects of the experimental setup for efficient probing of the electronic and structural dynamics in photocatalytic systems on multiple timescales.