Integration of unmanned aerial vehicles (UAVs) into fifth generation (5G) and beyond 5G (B5G) cellular networks is an intriguing problem that has recently tackled a lot of interest in both academia and industry. An effective solution is represented by cellular-connected UAVs, where traditional terrestrial users coexist with flying UAVs acting as additional aerial users, which access the 5G/B5G cellular network infrastructure from the sky. In this scenario, we study the challenging application in which an UAV acting as aerial user (AU) and a static (i.e., fixed) terrestrial user (TU) are paired to simultaneously transmit their uplink signals to a ground base station (BS) in the same time-frequency resource blocks. In such a case, due to the highly dynamic nature of the UAV, the signal transmitted by the AU experiences both time dispersion due to multipath propagation effects and frequency dispersion caused by Doppler shifts. On the other hand, for a static ground network, frequency dispersion of the signal transmitted by TU is negligible and only multipath effects have to be taken into account. To decode the superposed signals at the BS by using finite-length data record, we propose a novel sky-ground (SG) nonorthogonal multiple access (NOMA) receiving structure that additionally exploits the different circularity/noncircularity and almost-cyclostationarity properties of the AU and TU by means of improved channel estimation and time-varying successive interference cancellation. Numerical results demonstrate the usefulness of the proposed SG uplink NOMA reception scheme in future 5G/B5G networks.