The topology of the electronic band structure of solids can be described by its Berry curvature distribution across the Brillouin zone. We theoretically introduce and experimentally demonstrate a general methodology based on the measurement of energy- and momentum-resolved optical transition rates, allowing to reveal signatures of Berry curvature texture in reciprocal space. By performing time- and angle-resolved photoemission spectroscopy of atomically thin WSe₂ using polarization-modulated excitations, we demonstrate that excitons become an asset in extracting the quantum geometrical properties of solids. We also investigate the resilience of our measurement protocol against ultrafast scattering processes following direct chiroptical transitions. Here we provide the data presented in the paper referenced below. The data set contains the results of the first-principle calculations of the exciton properties, python scripts for solving the real-time dynamics, and python scripts for generating the plots. We also provide the raw measured photoemission intensity along with the post-processing and corresponding plotting scripts. A more detailed description is provided in the README.md files.