What is the purpose of the black paint below the cockpit windows?
It reduces glare (specular reflection).

Football players paint black stripes under their eyes for the same reason.



The legend for the paint scheme is excerpted in the inset, upper right. Item #33 "Antiglare areas shall be painted aircraft black."

If you read this technical manual, which is publicly available, it describes in the body of the text the use of anti-glare paint.