“Jazz wasn’t born on a particular day, it was created over a period of time. It wasn’t just one person or one race that was responsible for creating it. It was a meeting, and mixing, of the essences and emotions of many people, of many cultures.” 
A early example of jazz music that embodied this mixing of cultures is the lovely Creation of the World, written in 1923 by French composer, Darius Milhaud. Creation was written for ballet but was given an unmistakable jazz flavour some of the movements (particularly, the first, third and fourth). Leonard Bernstein has high praise for Creation, for the innovative way it blended the music of the European symphonic tradition with that of ragtime music bred in New Orleans. To quote Bernstein:
“Out of all this has comes a real masterpiece, one full-length, fully developed jazz work that has such character and originality that even today it sounds as fresh as it did when it was written in 1923 … Among all those experiments with jazz that Europe flirted with in this period, only The Creation of the World emerges complete, not as a flirtation but a real love affair with jazz.” 
Here is the first movement of Darius Milhaud’s The Creation of the World, performed by the Berlin Philharmonic Orchestra conducted by Sir Simon Rattle. Listen out for hints of Gershwin in Creation. This is no coincidence; Milhaud’s composition was written about the same time George Gershwin wrote Rhapsody in Blue.
And here is the 1st through 5th movement of Creation, performed under the baton of Leonard Bernstein:
 The Infinite Variety of Music, Amadeus Press, New York, 1962, 2007.