Timing synchronization (TS) is one of the key tasks in orthogonal frequency division multiplexing (OFDM) systems. However, multi-path uncertainty corrupts the TS correctness, making OFDM systems suffer from a severe inter-symbol-interference (ISI). To tackle this issue, we propose a timing-metric learning-based TS method assisted by a lightweight one-dimensional convolutional neural network (1-D CNN). Specifically, the receptive field of 1-D CNN is specifically designed to extract the metric features from the classic synchronizer. Then, to combat the multi-path uncertainty, we employ the varying delays and gains of multi-path (the characteristics of multi-path uncertainty) to design the timing-metric objective, and thus form the training labels. This is typically different from the existing timing-metric objectives with respect to the timing synchronization point. Our method substantively increases the completeness of training data against the multi-path uncertainty due to the complete preservation of metric information. By this mean, the TS correctness is improved against the multi-path uncertainty. Numerical results demonstrate the effectiveness and generalization of the proposed TS method against the multi-path uncertainty.