This paper investigates the random access procedure for non-terrestrial networks operating without global navigation satellite system (GNSS) support. In such scenarios, positioning uncertainties can reach several kilometers, which directly impacts the open-loop compensation mechanisms employed by the user equipment. To ensure that the resulting time and carrier frequency offsets can be handled by the network, the robustness of the standardized random access signal design and detection scheme must be enhanced. To extend radio access capabilities, identical Zadoff Chu (ZC) sequences are concatenated and then modulated into the orthogonal time frequency space (OTFS) modulation. Thanks to the specific characteristics of the OTFS-based random access signal, the received sequences are coherently combined, thereby maximizing the desired signal strength. Additionally, the proposed preamble minimizes the overhead associated with the cyclic prefix (CP) transmission. Numerical evaluations in a regenerative low-Earth-orbit (LEO) satellite scenario show that, despite significant positioning errors, the proposed OTFS random access design attains comparable peak-to-average power ratio (PAPR) and missed detection probability (MDP) to OFDM-based solutions, while improving spectral confinement and reducing overhead. These results demonstrate that the proposed OTFS-based random access design offers a robust and spectrally efficient alternative to OFDM for GNSS-independent NTN access.