How can I filter and sort by date in a dynamic view?

I've looked through the forums and see that filtering and sorting by dates in Dynamic view isn't a feature. Has anyone found a work around for that within the sheet you're pulling the data from?

I need to be able to have a checklist maintained and the date displayed in the dynamic view. It's easy enough to set that up, but it's entirely reliant on the fact that someone is constantly sorting the source sheet so the most recent date is on the top. Is there a way to auto-sort my source sheet? Is there a way to also be able to create a filter in the source sheet to pull in the current week's dates or something to that affect?