Next generation satellite payload technology is expected to provide digital processing capabilities. This will pave the way to regard satellites as flying base stations. However, the initial access procedure must be improved. In this work we focus on non-geostationary earth orbit (NGEO) satellite networks. In this scenario, the random access preamble signal and the detection must be robust to large carrier frequency offsets (CFOs). Towards this end, we investigate the adoption of the pruned discrete Fourier transform spread filter bank multicarrier waveform. The proposed design is suitable for the access scheme of forthcoming 5G-based NGEO satellite communications. The reason is twofold. First, it improves the spectral confinement with respect to the standard single-carrier frequency-division multiplexing (SC-FDM) waveform. Second, it achieves a high level of commonality with 5G new radio, by keeping unchanged the subcarrier spacing, the slot duration and the preamble sequence. Remarkably, the new design allows the straightforward application of non-coherent post detection integration (NCPDI) techniques, which divide the correlation in blocks. Numerical results show that the proposed solution reduces out-of-band emissions and the missed detection probability in presence of CFO, with respect to the conventional approach based on SC-FDM and preamble detection with full-length correlation.