As an important branch in Recommender System, occasional group recommendation has received more and more attention. In this scenario, each occasional group (cold-start group) has no or few historical interacted items. As each occasional group has extremely sparse interactions with items, traditional group recommendation methods can not learn high-quality group representations. The recent proposed Graph Neural Networks (GNNs), which incorporate the high-order neighbors of the target occasional group, can alleviate the above problem in some extent. However, these GNNs still can not explicitly strengthen the embedding quality of the high-order neighbors with few interactions. Motivated by the Self-supervised Learning technique, which is able to find the correlations within the data itself, we propose a self-supervised graph learning framework, which takes the user/item/group embedding reconstruction as the pretext task to enhance the embeddings of the cold-start users/items/groups. In order to explicitly enhance the high-order cold-start neighbors' embedding quality, we further introduce an embedding enhancer, which leverages the self-attention mechanism to improve the embedding quality for them. Comprehensive experiments show the advantages of our proposed framework than the state-of-the-art methods.