Non-terrestrial networks (NTN) are expected to play a key role in extending and complementing terrestrial 5G networks in order to provide services to air, sea, and un-served or under-served areas. This paper focuses the attention on the uplink, where terminals are able to establish a direct link with the NTN at Ka-band. To reduce the collision probability when a large population of terminals is transmitting simultaneously, we propose a grant-free access scheme called resource sharing beamforming access (RSBA). We study RBSA for low Earth orbit (LEO) satellite communications with massive multiple-input multiple-output (MIMO). The idea is to benefit from the spatial diversity to decode multiple overlapped signals. We have devised a blind and open-loop beamforming technique, where neither the receiver must carry out brute-force search in azimuth and elevation, nor are the terminals required to report channel state information. Upon deriving the theoretical throughput, we show that RBSA is appropriate for grant-free access to LEO satellite, it reduces the probability of collision, and thus it increases the number of terminals that can access the media. Practical implementation aspects have been tackled, such as the estimation of the required statistics, and the determination of the number of users.