This is what I meant when I don’t understand what you want exactly. Could you clarify what you are modeling? How many outputs do you want?
My logic is that you get, for every unit and time, a single value that summarizes the features with time-varying parameters, \theta_{i,t} = \alpha + \beta_t X_{i,t}. I’m not sure what you want to do with it from there. If you want one theta per time and unit, you can just ravel theta and you’re done. But when you say:
Do you mean that time is an index that counts up from 0 to 99? Do you just want a deterministic slope term in your model? In that case you would want to add the time index to your feature matrix and give it a coefficient.