We present an initialization method for variational quantum algorithms applicable to intermediate-scale quantum computers. The method explores the efficiently classically simulable Clifford points of a parameterized quantum circuit, using simulated annealing to find a low-energy initial state. We provide numerical evidence of the effectiveness of the technique for different choices of the Hamiltonian structure, number of qubits, and circuit depth. While a number of problems are considered, we note that the method is particularly useful for quantum chemistry problems, for which it is able to capture long-range correlation energy. The presented method could help achieve a quantum advantage in noisy or fault-tolerant intermediate-scale devices by preparing a high-quality initial state.