The evolution of next-generation wireless networks has spurred the vigorous development of the low-altitude economy (LAE). To support this emerging field while remaining compatible with existing network architectures, integrated sensing and communication (ISAC) based on 5G New Radio (NR) signals is regarded as a promising solution. However, merely leveraging standard 5G NR signals, such as the Synchronization Signal Block (SSB), presents fundamental limitations in sensing resolution. To address the issue, this paper proposes a two-stage coarse-to-fine sensing framework that utilizes standard 5G NR initial access signals augmented by a custom-designed sparse pilot structure (SPS) for high-precision unmanned aerial vehicles (UAV) sensing. In Stage I, we first fuse information from the SSB, Type\#0-PDCCH, and system information block 1 (SIB1) to ensure the initial target detection. In Stage II, a refined estimation algorithm is introduced to overcome the resolution limitations of these signals. Inspired by the sparse array theory, this stage employs a novel SPS, which is inserted into resource blocks (RBs) within the CORSET\#0 bandwidth. To accurately extract the off-grid range and velocity parameters from these sparse pilots, we develop a corresponding high-resolution algorithm based on the weighted unwrapped phase (WUP) technique and the RELAX-based iterative method. Finally, the density-based spatial clustering of applications with noise (DBSCAN) algorithm is adopted to prune the redundant detections arising from beam overlap. Comprehensive simulation results demonstrate the superior estimation accuracy and computational efficiency of the proposed framework in comparison to other techniques.