1 way could be to create a list of current month in a column(let's say B) using these formulas.

In B1

Formula: copy to clipboard
=EOMONTH(TODAY(),-1)+1


In B2 and copy down until to see blank cell plus(+)1 blank cell.

Formula: copy to clipboard
=IFERROR(IF(B1+1>EOMONTH(TODAY(),0),"",B1+1),"")


Use this list for your data validation.