It seems that you’re looking to get Month-to-date type of measurement. With Looker date/datetime filters you would have to change it every day.
The best way would be to create a siimple yes/no dimension called “is_month_to_date” and then use SQL dialect to calculate whether a record falls within the range you specified.
A more comprehensive approach would require building a so called calendar table, that could have the calculations already done and joining it to an explore would give you the information about MTD, WTD, or YTD straight away.
if its just a filter you want in the explore then set it to “is in the past” “2” “months”, this will filter to the current month which is not completed and the prior full month.