Will you only be selecting one date/month at a time, or will you want to be selecting multiple dates in the filter?
This is quite easy to achieve using a parameter if you only want to select one date at a time:
Create a parameter called DateChoice, and make it a Date type. Then create a calculated field along the lines below, which you can then filter on. You can extend the formula to include the other fields in your joined table. I've made it so that whatever date you choose, it just matches that month with DATETRUNC, but you can be as specific as you like. If you're reading your dates as they are from Excel, they are coming into Tableau as strings, so you will need to right click on each field and convert it to a date field.
DATETRUNC('month',[DateChoice]) = DATETRUNC('month',[Offer Accept Date]) OR
DATETRUNC('month',[DateChoice]) = DATETRUNC('month',[Application Date]) OR
DATETRUNC('month',[DateChoice]) = DATETRUNC('month',[Start Date])
A downside of this, is that the filter is always on, there is no "show all" option in the parameter, but you could have another parameter if you liked, to switch the date filter on and off.