Ultrasound sound-speed tomography (USST) has shown great prospects for breast cancer diagnosis due to its advantages of nonradiation, low cost, 3-D breast images, and quantitative indicators. However, the reconstruction quality of USST is highly dependent on the first-arrival picking of the transmission wave. Traditional first-arrival picking methods have low accuracy and noise robustness. To improve the accuracy and robustness, we introduced a self-attention mechanism into the bidirectional long short-term memory (BLSTM) network and proposed the self-attention BLSTM (SAT-BLSTM) network. The proposed method predicts the probability of the first-arrival time and selects the time with maximum probability. A numerical simulation and prototype experiment were conducted. In the numerical simulation, the proposed SAT-BLSTM showed the best results. For signal-to-noise ratios (SNRs) of 50, 30, and 15 dB, the mean absolute errors (MAEs) were 48, 49, and 76 ns, respectively. The BLSTM had the second-best results, with MAEs of 55, 56, and 85 ns, respectively. The MAEs of the Akaike information criterion (AIC) method were 57, 296, and 489 ns, respectively. In the prototype experiment, the MAEs of the SAT-BLSTM, the BLSTM, and the AIC were 94, 111, and 410 ns, respectively.