As a complement of terrestrial networks, non-terrestrial networks (NTN) have advantages of wide-area coverage and service continuity. The NTN is potential to play an important role in the 5G new radio (NR) and beyond. To enable the massive machine type communications (mMTC), the low earth orbit (LEO) satellite is preferred due to its lower transmission delay and path loss. However, the LEO satellite may generate notable Doppler shifts to degrade the system performance. Recently, orthogonal time frequency space (OTFS) modulation has been proposed. It provides the opportunity to allocate delay Doppler (DD) domain resources, which is promising for mitigating the effect of high mobility. Besides, as the LEO satellite constellation systems such as Starlink are thriving, the space spectrum resources have become increasingly scarce. Therefore, non-orthogonal multiple access (NOMA) is considered as a candidate technology to realize mMTC with limited spectrum resources. In this paper, the application of OTFS enabled NOMA for mMTC over the LEO satellite is investigated. The LEO satellite based mMTC system and the OTFS-NOMA schemes are described. Subsequently, the challenges of applying OTFS and NOMA into LEO satellite mMTC systems are discussed. Finally, the potential technologies for the systems are investigated.