In grant-free non-orthogonal multiple access, the set of active users is unknown a priori. We address the challenging problem of dynamic channel estimation in this context. Assuming that inactive users are completely muted (in order to avoid unwanted pilot/preamble interference on active users), we investigate a channel estimation method performed jointly with user activity detection, multi-user detection and decoding. Leveraging conditional independence assumptions in probabilistic modeling, we introduce a low-complexity channel estimation performing expectation propagation in parallel for the measurements over all receive antennas. The proposed channel estimation technique is evaluated under different receive antenna correlation models and shows a good performance/complexity tradeoff with respect to joint measurement processing.