Mass and spin are the only two parameters needed to completely characterize black holes (BHs) in general relativity. However, the interaction between BHs and their environment is where complexity lies, as the relevant physical processes occur over a large range of scales. That is particularly relevant in the case of supermassive black holes (SMBHs), hosted in galaxy centers, and surrounded by swirling gas and various generations of stars. These compete with the SMBH for gas consumption and affect both dynamics and thermodynamics of the gas itself. How the behavior of such a fiery environment influences the angular momentum of the gas accreted onto SMBHs, and, hence, BH spins, is uncertain. We explore the interaction between SMBHs and their environment via first three-dimensional sub-parsec resolution simulations (ranging from ~0.1 pc to ~1 kpc scales) that study the evolution of the SMBH spin by including the effects of star formation, stellar feedback, radiative transfer, and metal pollution according to the proper stellar yields and lifetimes. This approach is crucial in investigating the impact of star formation processes and feedback effects on the angular momentum of the material that could accrete on the central hole. We find that star formation and feedback mechanisms can locally inject significant amounts of entropy in the surrounding medium, and impact the inflow inclination angles and Eddington fractions. As a consequence, the resulting trends show upper-intermediate equilibrium values for the spin parameter of a ~= 0.6-0.9, corresponding to radiative efficiencies epsilon ~= 9%-15%. These results suggest that star formation feedback taking place in the circumnuclear disk during the infall alone cannot induce very strong chaotic trends in the gas flow, quite independently from the different numerical parameters.