Event-driven sensors such as LiDAR and dynamic vision sensor (DVS) have found increased attention in high-resolution and high-speed applications. A lot of work has been conducted to enhance recognition accuracy. However, the essential topic of recognition delay or time efficiency is largely under-explored. In this paper, we present a spiking learning system that uses the spiking neural network (SNN) with a novel temporal coding for accurate and fast object recognition. The proposed temporal coding scheme maps each event's arrival time and data into SNN spike time so that asynchronously-arrived events are processed immediately without delay. The scheme is integrated nicely with the SNN's asynchronous processing capability to enhance time efficiency. A key advantage over existing systems is that the event accumulation time for each recognition task is determined automatically by the system rather than pre-set by the user. The system can finish recognition early without waiting for all the input events. Extensive experiments were conducted over a list of 7 LiDAR and DVS datasets. The results demonstrated that the proposed system had state-of-the-art recognition accuracy while achieving remarkable time efficiency. Recognition delay was shown to reduce by 56.3% to 91.7% in various experiment settings over the popular KITTI dataset.