Nope... Every date in the calendar eventually falls on every day of the week.
January 4, 2010 falls in the first week of the year.
January the 10th falls on all days of the week at some point.
January 4 2010 falls on a Monday.
January 25, 2020 falls on a Saturday.
January 1st will be in the first week of January.
The first of the month can fall on any day of the week.
The first week in January
what day of the week was January 1st 1936
doce de mayo
Inauguration day is January 20, no matter which day of the week it falls on.
January 1st 1900 was a Monday.
January 1st 1905 was a Sunday.