In low-altitude surveillance and early warning systems, detecting weak moving targets remains a significant challenge due to low signal energy, small spatial extent, and complex background clutter. Existing methods struggle with extracting robust features and suffer from the lack of reliable annotations. To address these limitations, we propose a novel Temporal Point-Supervised (TPS) framework that enables high-performance detection of weak targets without any manual annotations.Instead of conventional frame-based detection, our framework reformulates the task as a pixel-wise temporal signal modeling problem, where weak targets manifest as short-duration pulse-like responses. A Temporal Signal Reconstruction Network (TSRNet) is developed under the TPS paradigm to reconstruct these transient signals.TSRNet adopts an encoder-decoder architecture and integrates a Dynamic Multi-Scale Attention (DMSAttention) module to enhance its sensitivity to diverse temporal patterns. Additionally, a graph-based trajectory mining strategy is employed to suppress false alarms and ensure temporal consistency.Extensive experiments on a purpose-built low-SNR dataset demonstrate that our framework outperforms state-of-the-art methods while requiring no human annotations. It achieves strong detection performance and operates at over 1000 FPS, underscoring its potential for real-time deployment in practical scenarios.