Dynamic driving scene reconstruction is critical for autonomous driving simulation and closed-loop learning. While recent feed-forward methods have shown promise for 3D reconstruction, they struggle with long-range driving sequences due to quadratic complexity in sequence length and challenges in modeling dynamic objects over extended durations. We propose UFO, a novel recurrent paradigm that combines the benefits of optimization-based and feed-forward methods for efficient long-range 4D reconstruction. Our approach maintains a 4D scene representation that is iteratively refined as new observations arrive, using a visibility-based filtering mechanism to select informative scene tokens and enable efficient processing of long sequences. For dynamic objects, we introduce an object pose-guided modeling approach that supports accurate long-range motion capture. Experiments on the Waymo Open Dataset demonstrate that our method significantly outperforms both per-scene optimization and existing feed-forward methods across various sequence lengths. Notably, our approach can reconstruct 16-second driving logs within 0.5 second while maintaining superior visual quality and geometric accuracy.