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This paper proposes a dynamic analytical initialization method for spacecraft attitude estimators. In the proposed method, the desired attitude matrix is decomposed into two parts: one is the constant attitude matrix at the very start and the other encodes the attitude changes of the body frame from its initial state. The latter one can be calculated recursively using the gyroscope outputs and the constant attitude matrix can be determined using constructed vector observations at different time. Compared with traditional initialization methods, the proposed method does not necessitate the spacecraft being static or more than two non-collinear vector observations at the same time. Therefore, the proposed method can promote increased spacecraft autonomy by autonomous initialization of attitude estimators. The effectiveness and prospect of the proposed method in spacecraft attitude estimation applications have been validated through numerical simulations.