Offline reinforcement learning (RL) has emerged as a promising framework for addressing robot social navigation challenges. However, inherent uncertainties in pedestrian behavior and limited environmental interaction during training often lead to suboptimal exploration and distributional shifts between offline training and online deployment. To overcome these limitations, this paper proposes a novel offline-to-online fine-tuning RL algorithm for robot social navigation by integrating Return-to-Go (RTG) prediction into a causal Transformer architecture. Our algorithm features a spatiotem-poral fusion model designed to precisely estimate RTG values in real-time by jointly encoding temporal pedestrian motion patterns and spatial crowd dynamics. This RTG prediction framework mitigates distribution shift by aligning offline policy training with online environmental interactions. Furthermore, a hybrid offline-online experience sampling mechanism is built to stabilize policy updates during fine-tuning, ensuring balanced integration of pre-trained knowledge and real-time adaptation. Extensive experiments in simulated social navigation environments demonstrate that our method achieves a higher success rate and lower collision rate compared to state-of-the-art baselines. These results underscore the efficacy of our algorithm in enhancing navigation policy robustness and adaptability. This work paves the way for more reliable and adaptive robotic navigation systems in real-world applications.