Whether you collect your data for years or just started, recent advancement in deep learning can help you get the best performance. There are two popular approaches to solve the small data problem.
Transfer learning technique allows us to leverage existing open datasets that are similar to the problem you're trying to solve to pretrain models that later can be fine-tuned for your particular data. This approach reduced the data needs even by a 1000 fold in case of images and recent research (Jan 2018) shows that it can reduce data needs by 100 times in case of Natural Language Processing (NLP).
GANs (Generative Adversary Networks) - this fancy named technique let us convert one set of images with labels into another one that better represents real-world examples. Think converting screenshots from documents into photos of such documents, Thanks to this technology iPhone X with FaceID is able to tell whether your eyes are looking at the screen or not. This kind of technique is best used with images but the attempts to apply it to text generation have limited success.