Grant-free access has the potential to reduce considerably the latency with respect to conventional contention-based access. However, in highly dynamic wireless networks, this paradigm comes with a number of new challenges, such as performing user activity detection and channel estimation directly upon packet arrival on top of symbol detection and decoding, due to limited signal overhead. In this paper, we consider an efficient hybrid message-passing algorithm, combining belief propagation with expectation propagation, to jointly perform all aforementioned tasks. A new expectation propagation message approximation rule is introduced for the sake of low-complexity Gaussian message-passing, without compromising the performance. Motivated by the need for non-orthogonal multiple access over frequency-selective channels, we validate the proposed scheme over a multi-antenna OFDM-interleave-division multiple access scenario. Numerical performance evaluations demonstrate the efficiency of the proposed method compared to existing ones in the same context.