How do I find the beginning of the week from an NSDate?

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you can use Calendar method date(from: DateComponents) passing [.yearForWeekOfYear, .weekOfYear] components from any date it will return the first day of the week from the calendar used. So if you would like to get Sunday just use Gregorian calendar. If you would like to get the Monday as the first day of the week you can use Calendar .iso8601 as you can see in this answer

Xcode 12 • Swift 5.3 or later (works with previous Swift versions as well)

extension Calendar {
    static let gregorian = Calendar(identifier: .gregorian)
}

extension Date {
    func startOfWeek(using calendar: Calendar = .gregorian) -> Date {
        calendar.dateComponents([.calendar, .yearForWeekOfYear, .weekOfYear], from: self).date!
    }
}

usage:

Date().startOfWeek()  // "Sep 20, 2020 at 12:00 AM"

If you would like to get the beginning of week at a particular timezone you just need to use a custom calendar:

var gregorianUTC = Calendar.gregorian
gregorianUTC.timeZone = TimeZone(identifier: "UTC")!
print(Date().startOfWeek(using: gregorianUTC))  // "2020-09-20 00:00:00 +0000\n"

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