Neural network got a lucky guess. Can it be trusted?
The loss in the curve suggests that the training can be improved by tuning hyperparameters, especially the learning rate and/or the batch size. Therefore the optimal decision would be to keep refining the model instead of using the already trained model.

If tuning hyperparameters is not an option, at least you should re-split training and validation data or at very least repeat with a different random seed.

If none of those is an option, you should take the best validation loss. The reason is that we are assuming that there is no leak of the validation data to the training data and that the validation data is representative of the data the model is going to be tested with. Without any other evidence, we should assume that the "sweet spot" you found would also lead to better results in a piece of test data the model has not seen before.