On the contrary, targeting childhood household income will see representation of the groups you're trying to help drop to nearly zero. Impoverished white children outscore wealthy black children by a significant margin on standardized tests, and there are a lot more poor white children than poor black children.
There used to be programs like that, and they mostly helped the children of Chinese and Vietnamese refugees from communism. Low childhood household income doesn't really have much effect - "low income" in a US context is quite rich in a world context.