Even areas in which my company can potentially benefit from Machine Learning, we don't have access to vast troves of data to use as training sets. So our brainstorming sessions have gone nowhere.
For finding a use case or at work just think of any normal problem like UI or ux design, or showing someone an enjoyable loading screen or funny picture, anyone can make something okay but to solve a problem close to optimally you start to need to gather data and do ml/ai
Where would I start with this? Is this even an ML problem?
Consider looking into traditional forecasting methods as a baseline. AR(I)MA based approaches with seasonality might actually be fine for you.
However, it all changes if there are structural breaks in your dataset. Look into Rob Hyndman's free online book (https://otexts.org/fpp2/) for an excellent introduction into timeseries forecasting.