I'm not sure this will be possible through a filter action since that will always filter us down to a single date. I'm happy to be proved wrong if someone else would like to chime in though.
I attached a workbook with a possible solution using a parameter to input the date value you want to filter to, and a calculated date field which keeps all dates previous to the selected date as well. On the Solution Dash, choose a date at the top, and both views will update accordingly with the proper running sum intact. This was the best I could come up with - I hope this helps!