Oxford has a "hurray" (spelled "hurrea") from Goldsmith in 1773 and "hurray" (thus spelled) from Thackerey in 1855. The OED finds the spelling "Hooray" from 1888.

As one who used to analyze this stuff as part of my job, I can say that I never encountered the USMC "OO-rah!" till the '90s.

Same for U.S. Army and Air Force "HOO-ah!" and U.S. Navy and Coast Guard "HOO-yah!"

Somebody must actually have gotten paid for introducing these.

During the Civil War, Confederates gave various "rebel yells" in battle, while Federals to have favored "Hurrah" and "Hurray."