I think I'm going to need more information here.
X-Pack ML can predict occurrences (counts of things), based upon established learned behavior (i.e. normally there is 2 items during this time period, 3 during the next time period, and so on).
However, you are seemingly describing a situation that may:
not actually have enough historical data to learn from - you say " expect certain files to be received within a particular week of the month" and "This process has been running for a few months now" which to me, states that there's only a handful of observations available (<8-12, because there's not that many weeks in a few months). ML, in general, needs a few hundred observations of a time series before computing a reliable model of behavior.
not be apparent that you're expecting a prediction on some attribute of the files (i.e. the number received). Can you clarify what feature of the file(s) you expect?