There’s nothing wrong in ignoring the stationary nature of the data and feeding it to the model. Laurence suggests training your model on the last few steps could yield better performance i.e. past the big event point since the last few data points more representational of future values (see this lecture) than the earlier ones.
Your understanding of stationary timeseries is correct. Given that trend and seasonality are the key factors behind making a stationary time series non-stationary, we can remove these components before building a model. Please look at the assignment for the week to get a better picture.