Abstract We present an analysis of the quenching of star formation in massive galaxies (M _* > 10^9.5 M _⊙) within the first 0.5–3 Gyr of the Universe’s history utilizing JWST-CEERS data. We utilize a combination of advanced statistical methods to accurately constrain the intrinsic dependence of quenching in a multidimensional and intercorrelated parameter space. Specifically, we apply random forest classification, area statistics, and a partial correlation analysis to the JWST-CEERS data. First, we identify the key testable predictions from two state-of-the-art cosmological simulations (IllustrisTNG and EAGLE). Both simulations predict that quenching should be regulated by supermassive black hole mass in the early Universe. Furthermore, both simulations identify the stellar potential (ϕ _*) as the optimal proxy for black hole mass in photometric data. In photometric observations, where we have no direct constraints on black hole masses, we find that the stellar potential is the most predictive parameter of massive galaxy quenching at all epochs from z = 0–8, exactly as predicted by simulations for this sample. The stellar potential outperforms stellar mass, galaxy size, galaxy density, and Sérsic index as a predictor of quiescence at all epochs probed in JWST-CEERS. Collectively, these results strongly imply a stable quenching mechanism operating throughout cosmic history, which is closely connected to the central gravitational potential in galaxies. This connection is explained in cosmological models via massive black holes forming and growing in deep potential wells, and subsequently quenching galaxies through a mix of ejective and preventative active galactic nucleus feedback.