The field of co-speech gestures synthesis is gaining more and more interest. However, many new systems utilize complex or resource-intensive architectures, making them impractical for integration into Embodied Conversational Agents (ECAs) or for exploration in fields like linguistics, where understanding the connection between speech and gestures is challenging. This paper introduces STARGATE, a novel architecture for Spatio- Temporal Autoregressive Graph from Audio-Text Embeddings. The model leverages autoregression for fast gestures generation, alongside graph convolutions and attention to integrate explicit structural knowledge and facilitate efficient spatial and temporal processing. Through both subjective and objective assessments against state-of-the-art models, our research demonstrates our model capabilities of generating convincing gestures fast. It also achieves slightly better scores in terms of credibility and coherence of generated gestures in relation to speech.