Graph neural networks (GNNs) have exhibited exceptional efficacy in a diverse array of applications. However, the sheer size of large-scale graphs presents a significant challenge to real-time inference with GNNs. Although existing Scalable GNNs leverage linear propagation to preprocess the features and accelerate the training and inference procedure, these methods still suffer from scalability issues when making inferences on unseen nodes, as the feature preprocessing requires the graph to be known and fixed. To further accelerate Scalable GNNs inference in this inductive setting, we propose an online propagation framework and two novel node-adaptive propagation methods that can customize the optimal propagation depth for each node based on its topological information and thereby avoid redundant feature propagation. The trade-off between accuracy and latency can be flexibly managed through simple hyper-parameters to accommodate various latency constraints. Moreover, to compensate for the inference accuracy loss caused by the potential early termination of propagation, we further propose Inception Distillation to exploit the multi-scale receptive field information within graphs. The rigorous and comprehensive experimental study on public datasets with varying scales and characteristics demonstrates that the proposed inference acceleration framework outperforms existing state-of-the-art graph inference acceleration methods in terms of accuracy and efficiency. Particularly, the superiority of our approach is notable on datasets with larger scales, yielding a 75× inference speedup on the largest Ogbn-products dataset.