Most do. Some never will. At about 4 weeks all of mine started developing preferences. Things they were fine with before were not at that age. Bottles, pacifiers, and having their head covered were three things they had no use for after that age.
Every baby is different, my six sure were. Some moms can be discreet even when not using a cover. Others seem to be obnoxiously brazen with how much of themselves they reveal, I’m guessing this mom falls into the latter category.