Machine learning methods for panel (longitudinal) data
Panel data = multi-object time series.
in other words you have time series problem (time) for different objects (obj) that you are trying to predcit (Y).
If I were you I would just dissect this problem and start thinking in terms of time-series + another discriminative column called obj. What approaches do you know there? Here is really cool and MODERN time-series tutorial, check it out.
Regarding NN, why are you trying to squeeze it in so hard? Let the data tell you what algo can model it. Personally given these 3 features NN is just too much and you can achieve similiar results with less complexity using some simpler/less expensive approaches.