Answer by taking a quote from the following article:

Bill "Bojangles" Robinson (May 25, 1878 - November 25, 1949) was an American tap dancer and actor, the best known and most highly paid African-American entertainer in the first half of the twentieth century. His long career mirrored changes in American entertainment tastes and technology. He started in the age of minstrel shows and moved to vaudeville, Broadway, the recording industry, Hollywood, radio, and television.

In 1928, a white impresario, Lew Leslie, produced Blackbirds of 1928 on Broadway, a black revue for white audiences starring Adelaide Hall and Bill Robinson along with Aida Ward, Tim Moore and other black stars. The show was a huge success on Broadway, where it ran for over one year to sell-out performances. On stage, Adelaide Hall and Robinson danced and sang a duet together, which captivated the audiences. From then on, Robinson's public role was that of a dapper, smiling, plaid-suited ambassador to the white world, maintaining a connection with the black show-business circles through his continuing patronage of the Hoofers Club, an entertainer's haven in Harlem. So successful was Adelaide Hall's collaboration with Bojangles, they even appeared together on stage at the prestigious Palace Theatre (Broadway) before they were teamed up together again by Marty Forkins (Robinson's manager) to star in another Broadway musical titled, "Brown Buddies", that opened in 1930 at the Liberty Theatre, where it ran for four months before commencing a road tour of the States. In 1939, Robinson returned to the stage in The Hot Mikado, a jazz version of the Gilbert and Sullivan operetta. The show opened at the Broadhurst Theatre, with Robinson cast in the role of the Emperor. His rendition of My Object All Sublime stopped the show and produced eight encores. After Broadway, the show moved to the 1939 New York World's Fair, and was one of the greatest hits of the fair. August 25, 1939, was named Bill Robinson Day at the fair. Robinson's next Broadway show, All in Fun (1940), was with an all-white cast. Despite having Imogene Coca, Pert Kelton, and other stars, the show received poor reviews at out-of-town tryouts in New Haven and Boston. When the white stars and co-producers, Phil Baker and Leonard Sillman, withdrew, Robinson became the star, the first time an African-American headlined an otherwise all-white production. Although the reviewers were enthusiastic about Robinson, they panned the show, and it failed to attract audiences. All in Fun closed after four performances.

When did Robinson get his opportunity on Broadway
Lew Leslie, produced Blackbirds of 1928 on Broadway, a black revue for white audiences starring Adelaide Hall and Bill Robinson along with Aida Ward,