Hey 03, great to see you've started your own trivia thread and a nice one at that! Wish I'd been around for the "Cactus Air Force" one of course. I'll re-start my thread tonight probably.
Okay, my answer:
Since The Marine Corps founded in 1775 was the Continental Marines, I'd say that's too late to say the colonial origins of the Corps.
As the colonies were British colonies my choice is that the United States Marine Corps traces its heritage to the British Royal Marines.
Although the current ranks of the Royal Marines number quite small compared to today's US Marines (7,000 vs. 175,000), both Corps of Marines have stood side by side in conflicts around the globe and maintain their close ties. Both Corps of Marines frequently have liaison officers on exchange with each other. The USMC emblem was loosely modeled from the Royal Marines. Neither Corps' emblems incorporates a shield signifying defense, unlike those of other services.
As 03, mentioned in the question that started this thread, during the war of 1812 with England, the British burned nearly every public building in Washington (including the White House and the Capital). The Marine Barracks were spared the burning out of respect.