This paper considers an uplink massive machine-type communication (mMTC) scenario, where a large number of user devices are connected to a base station (BS). A novel grant-free massive random access (MRA) strategy is proposed, considering both the sporadic user traffic and short packet features. Specifically, the notions of active detection time (ADT) and active detection period (ADP) are introduced so that active user detection can be performed multiple times within one coherence time. By taking sporadic user traffic and short packet features into consideration, we model the joint active user detection and channel estimation issue into a dynamic compressive sensing (CS) problem with the underlying sparse signals exhibiting substantial temporal correlation. This paper builds a probabilistic model to capture the temporal structure and establishes a corresponding factor graph. A novel sequential approximate message passing (S-AMP) algorithm is designed to sequentially perform inference and recover sparse signal from one ADT to the next. The Bayes active user detector and the corresponding channel estimator are then derived. Numerical results show that the proposed S-AMP algorithm enhances active user detection and channel estimation performances over competing algorithms under our scenario.