It was not until 1962 with the Engel v. White decision
Look Again.
https://en.wikipedia.org/wiki/McCollum_v._Board_of_Education
Years ago I read an excellent book on the subject called "The Myth of Separation" by David Barton.
It detailed how we got here from where we clearly were before. Basically it was the consequence of a bunch of Liars, and a lot of help from the 14th amendment.