Orthogonal time frequency space (OTFS) has emerged as the most sought-after modulation technique in a high mobility scenario. Sparse code multiple access (SCMA) is an attractive code-domain nonorthogonal multiple access (NOMA) technique. Recently a code-domain NOMA approach for OTFS, named OTFS-SCMA, is proposed. OTFS-SCMA is a promising framework that meets the demands of high mobility and massive connectivity. This paper presents a channel estimation technique based on the convolutional sparse coding (CSC) approach for OTFS-SCMA in the uplink. The channel estimation task is formulated as a CSC problem following a careful rearrangement of the OTFS input-output relation. We use an embedded pilot-aided sparse-pilot structure that enjoys the features of both OTFS and SCMA. The existing channel estimation techniques for OTFS in multi-user scenarios for uplink demand extremely high overhead for pilot and guard symbols, proportional to the number of users. The proposed method maintains a minimal overhead equivalent to a single user without compromising on the estimation error. The results show that the proposed channel estimation algorithm is very efficient in bit error rate (BER), normalized mean square error (NMSE), and spectral efficiency (SE).