Community detection is a key task in social network analysis, as it reveals the underlying structure and function of the network. Various global and local techniques exist for uncovering community structures in social networks wherein diffusion-based algorithms are proposed as novel methods for local community detection, particularly suited for large-scale networks. The efficacy of diffusion processes and initial detection is paramount in the successful identification of community structures within social networks. This effectiveness hinges significantly on the meticulous selection of the label diffuser core, which serves as the foundation for propagating labels through the network, and the precise labeling of boundary nodes. Addressing the constraints of current community detection algorithms, notably their time complexity and efficiency, this paper proposes a novel local community detection algorithm that combines core expansion with label diffusion, and deep embedding techniques. In the proposed method, a new centrality measure is introduced for appropriate core selection to facilitate precise label diffusion in the initial phase. Subsequently, a deep embedding technique is employed for updating labels of boundary and core nodes using the GraphSage embedding method. Finally, a rapid merging step is executed to amalgamate initially proximate communities into finalized community structures in large-scale social networks. We evaluate our algorithm on 14 real-world and 4 synthetic networks and show that it outperforms existing methods in terms of NMI, F-measure, ARI, and modularity. According to numerical results, the proposed method shows approximately 1.04 %, 1.03 %, and 1.12 % improvement in F-measure, NMI, and ARI measures respectively, compared to the second-best method, LBLD, in the networks with ground-truth. In addition, our method is able to accurately identify communities in large-scale networks such as Orkut, YouTube, and LiveJournal, where it ranks among the top-performing methods. Our approach exhibits the best performance in terms of ARI compared to other algorithms under comparison.