Two-dimensional (2D) spatial position of a vibration source in an optical distributed acoustic sensing (DAS) system can be determined based on a phase-sensitive optical time-domain reflectometer. However, due to interference and noise, this approach may acquire inaccurate arrival time information of the first arrival wave of the vibration source at different positions of the optical cable, resulting in large positioning errors. In this study, we propose a method of estimating the first arrival wave of the vibration source in a DAS system based on bilateral filtered edge detection. First, the spatio-temporal 2D signals collected by the DAS system were converted into a gray-scale map, and then the bilateral filtering method was used to reduce the noise. The edge features in the gray-scale image were extracted using a Canny operator-based edge detection method to obtain the first arrival time of the source. The proposed method can simultaneously consider the overall temporal and spatial characteristics of spatio-temporal 2D data and improve the accuracy of low signal-to-noise ratio signal of first arrival time pickup. Results show that for low signal-to-noise ratio signals affected by interference and system noise, the average error for pickup arrival time does not exceed 3 ms, pickup accuracy is higher than that of the traditional method; the algorithm takes only 0.1 s on average, and pickup time consumption is low.