It seems that you are confused about what the difference between a feature and a label is.
Your label is the 'gold' outcome that you are trying to predict. In stock prediction, this is often a single number, i.e. some form of regression. For a given time series you are trying to predict the price at a future point in time.
What you are suggesting is very well possible, and basically how (linear) regression works: given 300 data points, make a function that fits the data. Then get the value from the function from a given
x. LSTMs and other architectures are of course more complex, but the idea is similar.
You could, for instance, feed the prices of each time stamp as a feature to the LSTM. It should be a powerful predictor. The neural network will try to figure out which features are important at what stage in time.