I have seen two birthdays for the Green Berets – April 9, 1987 and June 19, 1952. This site wasn’t helpful: https://www.goarmy.com/special-forces.html. Wikipedia has the birthdate as April 9, 1987 – https://en.wikipedia.org/wiki/United_States_Army_Special_Forces.
YouTube video: Sgt Barry Sadler – Ballad of the Green Berets 1966 – YouTube
How the Green Berets got their name https://www.armytimes.com/off-duty/2020/07/14/how-the-green-berets-got-their-name/.
HAPPY BIRTHDAY TO THE SPECIAL FORCES BRANCH, CREATED APRIL 9, 1987 https://sofrep.com/news/happy-birthday-to-the-special-forces-branch-created-april-9-1987/.