I know this question is borderline alt history, but I've always been told that African-American soldiers were shocked by how they were treated as equals when serving under the French army. How come these experiences didn't result in more upheaval, while during WWII there wasn't this much integration (With the US forcing the Free French to segregate their forces).
One vital precondition for the success of the US civil rights movement was money; a second was votes. Black Americans amassed both by moving to northern and western states where they met less systematic (note, not “no”) discrimination.
The more black Americans lived in the north and west, the more educational and economic opportunities they got, and the more they accumulated money. The accumulation of education and money made the NAACP LDF, the organization dedicated to bringing test cases in court, possible; see the discussion of its 1925 origins in Boyle, ARC OF JUSTICE.
Likewise, the more black Americans lived in the north and west, the more important they were to politicians and specifically to Democratic politicians. Black migrants tended to move to cities, vital constituencies for Democratic representatives and presidential candidates. Beginning with 1932, Democratic presidential campaigns understood the importance of winning over black voters.
So: migration meant opportunity and political influence essential to the civil rights movement. Political importance led to the establishment of the Civil Rights Section in the Justice Department in 1939, which brought an important case to the Supreme Court, US v Classic, in 1941, to establish that federal civil rights law covered primary elections. The NAACP LDF brought a further case, Smith v Allwright, establishing in 1944 that all-white primaries were unconstitutional. This was a critical step, because throughout the South the Democratic primary was the election that really counted, and black people, to this point, were legally excluded. But no more.
That meant that now it was valuable to register black voters in the South. It’s pretty much a straight line from there to Freedom Summer, ie peak civil rights movement.
So: migration yielded opportunity and influence, which eroded segregationist law, which opened the door for movement organizing to really matter. And it was the world wars that enabled the largest migrations of black folks out of the South.