In uplink (UL) grant-free sparse code multiple access (SCMA) systems, unlike the conventional contention-based transmission, users' activities should be known be-fore data decoding due to sporadic transmission in massive machine-type communication (mMTC). Since compressed sensing (CS) is the theory of sparse signal reconstruction with fewer samples, this theory is a good solution to de-tect active users. In this paper, we propose the dynamic and sparsity adaptive compressed sensing (DSACS) based active user detection (AUD) and channel estimation (CE) of UL grant-free SCMA. Unlike most of the CS-based methods, sparsity knowledge or potential active user list is not needed in the proposed algorithm, which is already not known in the practical systems. The proposed algorithm adopts a stage-wise approach to expand the set of accurate active users for adaptively achieve the sparsity level. It uses the temporal correlation of users' activity to improve performance and re-duce complexity. Then, false detected users are eliminated with joint message passing algorithm (JMPA), and channel gains of the accurate active users are estimated again in CE with feedback. The simulation results show that the proposed method without sparsity knowledge is capable of achieving detection in various scenarios in case of sporadic transmis-sion in mMTC.