So here's some math for you. Before we get to it, let's look at some historiography courtesy of University of Minnesota professor Steven Ruggles and his article "The Origins of the African-American Family Structure." Ruggles alludes to some of the earlier data and what I suspect were Thomas Sowell's sources:
The controversy over the Moynihan report stimulated a spate of revisionist historical investigations into African-American family structure. These studies asserted that Black families in the late nineteenth century were overwhelmingly male-headed and nuclear in structure. Although some authors acknowledged minor differences in family structure between Blacks and Whites, they all maintained that in practical terms Black families were essentially similar to White families (Agresti 1978; Bigham 1981; Carlson 1988; Furstenberg, Hershberg, and Modell 1975; Gutman 1975, 1976; Harris 1976; Krech 1982; Lammermeir 1973; Pleck 1972; Riley 1975; Shifflett 1975). The revisionists thus implied that the distinctive African-American family pattern is of recent origin, and this reinforced the now widespread view that economic disadvantages faced by Blacks in the recent past are responsible (Brewer 1988; Wilson 1987).
This actually helps me because I've long wondered why sociological work on Black families seemed so ahistorical. There's a strong bias toward looking at Black people through the lens of the 1960s--as though Black America begins with the Long Hot Summers. I suspect part of that is that we just didn't have great data on Black families, and the data we had indicated that something had gone drastically "wrong" around 1960.
But while it's true that you see a dramatic increase in single-family homes in 1960, the gap is about as old as our data. Ruggles was able to get ahold of census micro-data and basically concluded as much. If you look at the report you can see on Table 2 that as early as 1880 there were roughly double the percentage of Black children born to single mothers as to Whites (13.1 to 5.9.) Ruggles concludes:
...[T]he finding of recent studies that the high incidence of single parenthood and children residing without parents among Blacks is not new. The pattern is clearly evident as far back as 1850 among free Blacks. From 1880 through 1960, the percentage of Black children with at least one absent parent was fairly stable and about two-and-one-half times greater than the percentage among Whites. Recently, the percentages of both Black children and White children with absent parents have risen dramatically...
Race differences in family structure have expanded throughout the twentieth century, especially over the past three decades. But the fundamental differences in the percentage of children residing without parents began well over a century ago. The critical question remains: What is the source of this distinctive African-American pattern of single parenthood? Recent economic changes can be invoked to explain the growing differential between Black family structure and white family structure, but they cannot explain why Blacks started from a higher base.
Again, you see a big shift in 1960. But that's true for both Black and White families, and it's a shift that has been oft-commented upon. The change in marriage is not a "Black" problem, and I am not even convinced that it is a "problem." People who want us to go back to 1880 should have the intellectual courage to advocate for the entirety of their vision, not just the parts they like. It is not simply a question of "Is marriage good for kids?" It's "Are shotgun marriages good for kids?" "Should marriage be valued at all costs, including enduring abuse or ill-treatment?" "Should women marry men regardless of their employment prospects and their contact with the correctional system?"