How to enter Edit mode when zero web parts using a GET request?

Finally I bumped into the answer after looking at the url presented after creating a new web part page :-)

Place these querystring arguments on any Web Part page and you enter edit mode:

PageView=Shared&ToolPaneView=2

Example: http://www.domain.com/default.aspx?PageView=Shared&ToolPaneView=2

That's it!