Best ML model for predicting yearly data with many blocks?
Your data consists of time series. Recurrent neural networks, RNNs, are applied successfully to problems like this data. Its structure is appropriate for you. Especially, you can use LSTM which is very powerful for time series data. Also there are a lot of papers in arxiv about its capabilities, pros and cons.

I think, linear regression can fail for your task.

I suggest you to read this and this articles to understand how LSTM works and what you can do with it. Then you can decide is it appropriate for your problem or not.