I have the same requirement. I was wondering if you were able to find a solution?
Go through below link
We don't have option of default value for Quick filter, but use the use the following steps it will give you near solution to your query.
1) Create a calculation
Name :Week No
"Week " + if datepart("week", [Date]) <= datepart("week", today()) then str(datepart("week", [Date])) end
2) Create another calculation
Name: Lees than or Equal of current week
Syntax: date([Date]) <= date(today())
3) Drag Week No onto Row shelf, drag Lees than or Equal of current week onto filter shelf then select TRUE
4) right click on Week No, click on Sorting. select "Descending"