Probably not what you have in mind, but in Israel, the week does start on Sunday. (Sunday is also literally translated to "First Day" in Hebrew). I believe tha

Probably not what you have in mind, but in Israel, the week does start on Sunday. (Sunday is also literally translated to "First Day" in Hebrew). I believe that this is also the case in other countries. I think the weekend being Saturday-Sunday is specifically a Christian thing, with Saturday being a day of rest an originally Jewish thing, and that other countries have different weekends.