Suicidal ideation detection is a vital research area that holds great potential for improving mental health support systems. However, the sensitivity surrounding suicide-related data poses challenges in accessing large-scale, annotated datasets necessary for training effective machine learning models. To address this limitation, we introduce an innovative strategy that leverages the capabilities of generative AI models, such as ChatGPT, Flan-T5, and Llama, to create synthetic data for suicidal ideation detection. Our data generation approach is grounded in social factors extracted from psychology literature and aims to ensure coverage of essential information related to suicidal ideation. In our study, we benchmarked against state-of-the-art NLP classification models, specifically, those centered around the BERT family structures. When trained on the real-world dataset, UMD, these conventional models tend to yield F1-scores ranging from 0.75 to 0.87. Our synthetic data-driven method, informed by social factors, offers consistent F1-scores of 0.82 for both models, suggesting that the richness of topics in synthetic data can bridge the performance gap across different model complexities. Most impressively, when we combined a mere 30% of the UMD dataset with our synthetic data, we witnessed a substantial increase in performance, achieving an F1-score of 0.88 on the UMD test set. Such results underscore the cost-effectiveness and potential of our approach in confronting major challenges in the field, such as data scarcity and the quest for diversity in data representation.