The matter-antimatter asymmetry underlines the incompleteness of the current understanding of particle physics. Neutrinoless double-beta (0νββ) decay may help explain this asymmetry, while unveiling the Majorana nature of the neutrino. The CUORE experiment searches for 0νββ decay of ¹³⁰Te using a tonne-scale cryogenic calorimeter operated at milli-kelvin temperatures. We report no evidence for 0νββ decay and place a lower limit on the half-life of T_1/2 > 3.8 × 10²⁵ years (90% C.I.) with over 2 tonne⋅year TeO₂ exposure. The tools and techniques developed for this result and the 5 year stable operation of nearly 1000 detectors demonstrate the infrastructure for a next-generation experiment capable of searching for 0νββ decay across multiple isotopes.