When you need to refer to a specific week, you can pick a day that falls during that week, and call it "the week of (that date)":

I think we're coming the week of June 4th.

Usually you use the first day of the week (Monday) as the date in this expression. But you can also use other days of the week. If you only remember one date during that week, you can use that date, whether it's the first day of the week or not.