In this paper, we present a novel dynamic bandwidth allocation (DBA) scheme for future generation passive optical networks (PON) in order to meet the beyond 5G (B5G) and sixth generation (6G) stringent requirements. Our proposed algorithm is a generalized multi-access DBA (GMA-DBA) that exploits both orthogonal and non-orthogonal multi-access (MA) resources, resulting in a radical enhancement in the network performance. The proposed GMA-DBA algorithm is modeled as an optimization problem for which a closed form solution is derived. Results show that the GMA-DBA is capable of accommodating a network throughput higher than 1 Tbps while securing a latency and jitter below 100 µs and 10 µs, respectively. It can also maintain reliability, simplicity and energy efficiency. Therefore, using a non-orthogonal MA layer seems to be inevitable to achieve the stringent performance needed for the B5G and 6G next generation systems.