Well, black slaves associated themselves with the Exodus narrative pretty early on, but if you're wondering about those groups that claim blacks are the real Jews (referred to as Black Hebrew Israelites on Wikipedia), the earliest explicit ones came in the 1880s and 1890s, the most prominent name among them being William Saunders Crowdy, a former slave from Maryland. His movement, like many of the others in the late 19th century, began with receiving a vision that told him that Jesus and the Biblical Israelites were black, and that those brought to the Americas in the Atlantic Slave Trade were descendants of the black Israelites. These teachings were appropriated by more black nationalist/separatist movements in the 1910 through the 1930s, when the Ethiopian Hebrew Congregations came into being. I made a YouTube video about it earlier this year. Here is a link to the footnoted script I used for the video. https://drive.google.com/open?id=1f4zzTKf0Cc3p128csbyK0U2V-5ogUvDAH_Gtjx-63gk Here is the video version of that if you are interested. https://youtu.be/LeF1d3BONmo