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Recent studies show that depression can be partially reflected from human facial attributes. Since facial attributes have various data structure and carry different information, existing approaches fail to specifically consider the optimal way to extract depression-related features from each of them, as well as investigates the best fusion strategy. In this paper, we propose to extend Neural Architecture Search (NAS) technique for designing an optimal model for multiple facial attributes-based depression recognition, which can be efficiently and robustly implemented in a small dataset. Our approach first conducts a warmer up step to the feature extractor of each facial attribute, aiming to largely reduce the search space and providing customized architecture, where each feature extractor can be either a Convolution Neural Networks (CNN) or Graph Neural Networks (GNN). Then, we conduct an end-to-end architecture search for all feature extractors and the fusion network, allowing the complementary depression cues to be optimally combined with less redundancy. The experimental results on AVEC 2016 dataset show that the model explored by our approach achieves breakthrough performance with 27\% and 30\% RMSE and MAE improvements over the existing state-of-the-art. In light of these findings, this paper provides solid evidences and a strong baseline for applying NAS to time-series data-based mental health analysis.