Obstacle avoidance in complex and dynamic environments is a critical challenge for real-time robot navigation. Model-based and learning-based methods often fail in highly dynamic scenarios because traditional methods assume a static environment and cannot adapt to real-time changes, while learning-based methods rely on single-frame observations for motion constraint estimation, limiting their adaptability. To overcome these limitations, this paper proposes a novel framework that leverages multi-frame point constraints, including current and future frames predicted by a dedicated module, to enable proactive end-to-end navigation. By incorporating a prediction module that forecasts the future path of moving obstacles based on multi-frame observations, our method allows the robot to proactively anticipate and avoid potential dangers. This proactive planning capability significantly enhances navigation robustness and efficiency in unknown dynamic environments. Simulations and real-world experiments validate the effectiveness of our approach.