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Recently, a few novel streaming attention-based sequence-to-sequence (S2S) models have been proposed to perform online speech recognition with linear-time decoding complexity. However, in these models, the decisions to generate tokens are delayed compared to the actual acoustic boundaries since their unidirectional encoders lack future information. This leads to an inevitable latency during inference. To alleviate this issue and reduce latency, we propose several strategies during training by leveraging external hard alignments extracted from the hybrid model. We investigate to utilize the alignments in both the encoder and the decoder. On the encoder side, (1) multi-task learning and (2) pre-training with the framewise classification task are studied. On the decoder side, we (3) remove inappropriate alignment paths beyond an acceptable latency during the alignment marginalization, and (4) directly minimize the differentiable expected latency loss. Experiments on the Cortana voice search task demonstrate that our proposed methods can significantly reduce the latency, and even improve the recognition accuracy in certain cases on the decoder side. We also present some analysis to understand the behaviors of streaming S2S models.