You can anonymize your data. See this video:
If we need to go to a packaged workbook, that's what you can do to help someone help you.
But first help me understand what you are saying. If you pick a date through your filter, and if there is no data on that date, Tableau picks your next date where there actually IS data to start your chart. And you want to see the chosen date as your starting point, no matter how far in the future your first actual data point is.
Is that correct?
You can add a reference line equal to the chosen starting date. You can tell tableau not to label it, and not to show it. By doing that, you force a mark on the chart at the chosen starting date, and tableau will obey that.