If this were a special case -- say, one class in 100 was represented by a single training image -- then you might get away with it. However, a unique image per class is asking for trouble.
A neural network learns by iterative correction, figuring out what features and combinations are important, and which are not, in discriminating the classes from one another. Training starts by a chaotic process that has some similarities to research: look at the available data, form hypotheses, and test then against the real world.
In a NN, the "hypotheses" are the various kernels it develops. Each kernel is a pattern to recognize something important to the discrimination process. If you lack enough examples for the model to generalize and discriminate for each class, then you run the risk (actually, you have the likelihood) of the model making a conclusion that is valid for the one input image, but not others in the same class.
For instance, one acquaintance of mine did the canonical cat-or-dog model, using his own photos, showing the pets of his own household and those of a couple of friends. The model trained well, identified cats and dogs with 100% accuracy on the test data, and he brought it into work ...
... where it failed, having an accuracy of about 65% (random guessing is 50%). He did some analysis and found the problem: his friends have indoor cats, but their preferred dog photos were out of doors. Very simply, the model had learned to identify not cats vs dogs, but rather couches and kitchen cabinets vs outdoor foliage. One of the main filters was of large, textured, green areas. Yes, a dog is a large, textured, green being. :-)
The only way your one-shot training would work is if each of your training images was specifically designed to include exactly those features that differentiate this class from the other 299, and no other visual information. Unfortunately, to identify what features those might be, and to provide canonical training photos, you'd have to know in advance what patterns the model needed to pick.
This entirely defeats the use case of deep learning and model training.