Forecasting a target with a non-datetime index

Sorry in advance for the novel lol.

Have a question about TS (or alternatives) for forecasting a target where the "time" index is just an ordered integer sequence denoting days since an employee was hired ("tenure days"), and where no data exists yet for the later tenure stages (new process, see notes below).

We are trying to model the average productivity ramp-up period during the first year post-hire for manufacturing workers. For every worker, we have a daily record of …

advance data datascience datetime employee forecasting index notes novel process question tenure