Actually, Brown v. Board of Education did not start the Civil Rights movement. The Civil Rights Movement in the United States is older than the nation. On April 6, 1712, slaves in New York City revolted against their masters. Over 70 blacks were rounded up and 21 convicted and sentenced to death -- 20 were executed by being burned alive and the 21st was broken on the wheel. Free blacks were forbidden to own property and blacks were not allowed to gather in groups of three or more. Other slave revolts followed. On April 14, 1775, 24 men, mostly Quakers, formed the Pennsylvania Society for the Relief of Free Negroes Unlawfully Held in Bondage, which fought for abolition. The NAACP was formed Feb. 12, 1909, and was, in turn, birthed by earlier civil rights movements and leaders. CORE (the Congress of Racial Equality) was founded in 1941, and sent their first Freedom Riders (mixed groups of white and black bus riders) South on April 10, 1947. The point of the above is that the Civil Rights movement started long before the success of Brown v. Board of Education in 1954.
And, in discussing the Civil Rights movement, you have to understand the role of World War 1 and particularly World War 2 played in the movement. Blacks were drafted into the American military for both wars, with the Harlem Hellfighters serving under French command at the front during World War 1. When these soldiers returned to the United States following WW1, they provided new impetus to the Civil Rights movement, sparking race riots across the nation, particularly in Tulsa and Chicago, as they refused to be treated as second-class citizens. The effect following World War 2 was much greater, since American combat involvement was limited to six months in WW1 and was close to four years in WW2. Men like Jackie Robinson, who was court-martialed as a young Army lieutenant for refusing to give up his seat on a bus, refused to be shot at in the name of freedom and then have the freedoms they fought and died for refused to them. These two wars, more than anything, helped spark the Civil Rights movement in the 50s and 60s.
Further Brown vs. Board of Education did not exist in a vacuum, but was the result of a series of cases aimed at overturning the 1896 ruling of Plessy v. Ferguson. In 1917, the Supreme Court ruled in Buchanan vs. Warley that "separate but equal" segregated housing violated the 14th Amendment, chipping away at Plessy. Starting with Buchanan, the NAACP and other civil rights organizations brought a series of cases to the Supreme Court that made Plessy untenable. These cases include Murray v. Pearson, Mitchell v the United States, Missouri ex rel. Gaines v. Canada, Morgan v. Virginia, Sipuel v. Board of Regents of the University of Oklahoma, McLaurin v. Oklahoma State; Sweatt v. Painter and Henderson v. United States. On Sept. 4, 1952, 11 black students enroll in the previously segregated Claymont High School in Delaware. There is no outcry in the community and the day passes peacefully and without incident. The next day, the Delaware AG tells Claymont officials that the case is being appealed through the courts and the students will have to go home. School Superintendent Harvey Stahl and the school board disagreed and two of the 11 students who entered the high school graduated just before the Supreme Court handed down its ruling in Brown.
So, to say that Brown v. Board of Education started the Civil Rights movement ignores a lot of history behind the movement, including the slave revolts and abolition movements, and ignores a lot of the case law that was developed to get Plessy v. Ferguson overturned.