Getting an Average Point In Time by Date and Individual

First thing I would do is split the Date/Time column into its respective Date and Time components. You can keep the original column if you wish, but splitting these columns should make your life easier.  Time is a data type which is considered numeric, so you can run the standard Average functions over it, as well as Min.

To get Average first scan time we would use a formula like this:

Average First Scan by Person = AVERAGEX(
    VALUES('YourData'[Person],
    MIN('YourData'[ScanTime])
)

Average First Scan by Day = AVERAGEX(
    VALUES('YourData'[ScanDate],
    MIN('YourData'[ScanTime])
)

So with measures like this, you can apply a filter context to make them do what you want.  For example, if you select a single person and use the measure "Average First Scan by Day", you'll get a persons average start time.  You could then additionally filter the date for a range and see what the average was for a specific period.

Hopefully this concept makes sense to you and you can apply it in a way that makes sense to your data and model.