I hope I'm understanding your question...
Using API /2/events/, set the parameter "
time" with the first value an absolute time in milliseconds for the first day of the month. The API doesn't have a way to compute the time you'll need to supply, so do that however your language would do it. For example, I use "Date::Calc" module in Perl to convert a date into a time value (multiply by 1000 to get milliseconds). Time-zone may complicate matters a bit. I think they will use UTC, but I am not sure.
Alternative is if you know the day of the month (e.g. today is the 8th November, then you can probably use a relative time value such as "-8d" is 8 days before today. Try it and see "time=-8d," (nothing after comma means unbounded to future). If you don't want all future beyond this month, I guess you also need to bound the second parameter, but then you need to use come other module (like Perl's "Date::Calc") to figure out the number of days to the end of the month.