Organized in 1884, the first African American professional baseball team was the Cuban Giants.

Is was the Cuban Giants a phrase?

No. Didn't I already answer this below? It's the complete predicate.

http://grammar.ccc.commnet.edu/grammar/objects.htm#predicate

No.

Study this explanation and list of prepositions.

http://www.chompchomp.com/terms/preposition.htm

No, "Cuban Giants" is not a phrase in the traditional sense. It refers to an actual baseball team that existed in the late 19th century. The Cuban Giants were indeed the first professional African American baseball team, organized in 1884. They played primarily in the northeastern United States and were composed mostly of African American and Afro-Latino players. The team name was derived from the fact that many of the players were of Cuban descent or had Cuban connections. They were pioneers in breaking racial barriers in professional sports during a time when segregation was prevalent in American society.