Until now many regions around the world are still uncovered by cellular terrestrial mobile system services due to the lack of economic feasibility as well as the difficulty of introducing such services. Conversely, a large geographic region can be covered by using only a single satellite, so it is worthwhile to extend the actual terrestrial services using satellite system. The new hybrid integrated “terrestrial-satellite” cellular system, known under the name of Non-Terrestrial Networks (NTN), will see the light with the support of future 6G technology. It is expected that 6G cellular mobile system will play the role of integrating terrestrial, aerial, maritime, and space communications into a universal network that could support a massive number of terminals with ultra-low latency. For the realization of the NTN system, new technologies should be introduced at the level of terrestrial cellular network, arial network, and satellite network. One of these promising technologies is represented by an efficient multiplexing technique known under the name of non-orthogonal multiple access (NOMA). With this technique, multiple users can be served on a single time-frequency resource block by using the concepts of superposition coding at the transmitter and successive interference cancellation (SIC) at the receiver. Moreover, NOMA has an achievable performance gain in terms of spectral efficiency over the traditional orthogonal multiple access (OMA) technique. Evaluation of a NOMA-based NTN system supported by 6G technologies in terms of system parameters and channel capacity represent the main objective of this paper.