How to manually control when the first week of the year begins?

=WEEKNUM(A1)-IF(WEEKDAY(YEAR(A1))=1,0,1)

=WEEKNUM(TODAY())-IF(WEEKDAY(YEAR(TODAY()))=1,0,1)

Assumes A1 is a valid date. TODAY() can be substituted for A1

WEEKNUM returns 1 to 54 corresponding to start of year and Sunday (or other days with modifiers).

No problem if year starts on Sunday, otherwise when Sunday rolls around week count is off by 1.

If Jan 1 of present year is not a Sunday, subtract 1 from week count.

This formula makes the first days of the year as week 0.

=WEEKNUM(A1)-AND(IF(WEEKDAY(YEAR(A1))=1,0,1),WEEKNUM(A1)<>1)

We take advantage of AND and data is 1 (boolean) to mask out (AND) correction for first days of year. Week should go from 1 to 52 (53?). First Sunday in year will be Week 1 and previous days will be week 1. Week 1 could be 13 days long!