I would all the dates of the current month to be listed in a column, updated to the next month on the 1st of the month, and no requirement for me to input anything into the system. I've played around with multiple IF functions and different date formulas but can't get anything to work.
In your first cell, rebuild the first date of the month by forcing 1 as the date and reusing the year and month of the current date:
=DATE(YEAR(TODAY()), MONTH(TODAY()), 1)
In the next 30 cells, use and drag this:
=IFERROR(IF(MONTH(A1+1)=MONTH(A1),A1+1,""), "")
I'm sure there's a cleaner way but I can't be bothered.