Satellite communication system is expected to play a vital role for realizing various remote internet of things (IoT) applications in 6G vision. Due to unique characteristics of satellite environment, one of the main challenges in this system is to accommodate massive random access (RA) requests of IoT devices while minimizing their energy consumptions. In this paper, we focus on the reliable design and detection of RA preamble to effectively enhance the access efficiency in highdynamic low-earth-orbit (LEO) scenarios. To avoid additional signaling overhead and detection process, a long preamble sequence is constructed by concatenating the conjugated and circularly shifted replicas of a single root Zadoff-Chu (ZC) sequence in RA procedure. Moreover, we propose a novel impulse-like timing metric based on length-alterable differential cross-correlation (LDCC), that is immune to carrier frequency offset (CFO) and capable of mitigating the impact of noise on timing estimation. Statistical analysis of the proposed metric reveals that increasing correlation length can obviously promote the output signal-to-noise power ratio, and the first-path detection threshold is independent of noise statistics. Simulation results in different LEO scenarios validate the robustness of the proposed method to severe channel distortion, and show that our method can achieve significant performance enhancement in terms of timing estimation accuracy, success probability of first access, and mean normalized access energy, compared with the existing RA methods.