Proactive streaming video understanding requires Video-LLMs to decide when to respond as a video unfolds, a task where existing methods often fall short due to their implicit, query-agnostic modeling of visual evidence. We introduce Response-G1, a novel framework that establishes explicit, structured alignment between the accumulated video evidence and the query's expected response conditions via scene graphs. The framework operates in three fine-tuning-free stages: (1) online query-guided scene graph generation from streaming clips; (2) memory-based retrieval of the most semantically relevant historical scene graphs; and (3) retrieval-augmented trigger prompting for per-frame "silence/response" decisions. By grounding both evidence and conditions in a shared graph representation, Response-G1 achieves more interpretable and accurate response timing decisions. Experimental results on established benchmarks demonstrate the superiority of our method in both proactive and reactive tasks, validating the advantage of explicit scene graph modeling and retrieval in streaming video understanding.