How to pivot my data and get counts based on the min and max date value

I haven't fully validated this, but on first glimpse it seems to work (if I understood correctly)

For the pivot 'values' you can use a filter within a formula using the syntax documented here

On [Days in Date] click 'Edit Filter' to apply a Bottom 1 rank filter on MIN([Days in Date])

Duplicate the value for "End Date", and change the filter to be Top 1 rank filter on MAX([Days in Date])

Check your numbers match what you expect 😀