A long standing puzzle is whether information is lost after black holes evaporate, contradicting the unitarity of quantum mechanics. Don Page proposed a solution to this paradox by suggesting that the black hole and its emitted radiation can be effectively described by a random state of qubits. Building upon this framework, our study delves into the implications of unitarity on global symmetries within evaporating black holes. To achieve this goal, we employ the concept of entanglement asymmetry as a modern, information-based metric of symmetry breaking. Our findings reveal that, in the absence of any symmetry, a U(1) symmetry emerges, remaining exact up to the thermodynamic limit prior to the Page time. At the Page time, the entanglement asymmetry shows a finite jump to a large value. This implies that the radiation emitted by the black hole exhibits symmetry until the Page time, beyond which it undergoes a sharp transition.