I know it might feel redundant, but is it possible to just create another column with the dates you want to merge on? So the collapsed data would have two columns, one with the first date observed (2020-01-03) and another with the first day of the month (2020-01-01)?
Another option, that basically is the same as what I suggested but might be cleaner is to use MonthlyDates.jl, which would allow you to just use the month-year combination.