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Deep Neural Networks (DNNs) are vulnerable to adversarial examples, which are crafted by adding human-imperceptible perturbations to the benign inputs. Simultaneously, adversarial examples exhibit transferability across models, enabling practical black-box attacks. However, existing methods are still incapable of achieving the desired transfer attack performance. In this work, focusing on gradient optimization and consistency, we analyse the gradient elimination phenomenon as well as the local momentum optimum dilemma. To tackle these challenges, we introduce Global Momentum Initialization (GI), providing global momentum knowledge to mitigate gradient elimination. Specifically, we perform gradient pre-convergence before the attack and a global search during this stage. GI seamlessly integrates with existing transfer methods, significantly improving the success rate of transfer attacks by an average of 6.4% under various advanced defense mechanisms compared to the state-of-the-art method. Ultimately, GI demonstrates strong transferability in both image and video attack domains. Particularly, when attacking advanced defense methods in the image domain, it achieves an average attack success rate of 95.4%. The code is available at $\href{https://github.com/Omenzychen/Global-Momentum-Initialization}{https://github.com/Omenzychen/Global-Momentum-Initialization}$.