I'm currently studying race theory in American politics and how organizations try to empower certain demographics. Were there any ancient entities that tried to implement solutions to domestic problems? Or was it usually left to the sovereigns or local heads of state head to deal with issues?
Sort of! Public giving was very important in the Hellenistic and Roman world, but it didn't work like a modern charity. Elites gave sometimes vast sums of money to build public buildings, hold public festivals, and fund grain doles in cities around the Mediterranean. But these gifts weren't aimed at uplift. Many of the buildings, like libraries, were aimed at the upper classes. Handout programs like grain doles usually only benefitted citizens who had established residence in a city for some time and could prove it by being on registered lists and showing a token that proved their right to free or discounted food (if you were a beggar, you weren't getting free grain). In Rome, the emperor paid for much of this public generosity. In smaller cities, the local elites got to show off.
This was, for the elites, about building their reputation, demonstrating their power and influence, and securing the loyalty of networks of clients who could lend valuable boots-on-the-ground support when needed. In Rome, it demonstrated the power and wealth of the emperor, and a few choice elites who were allowed to share in the responsibility.
None of these programs really targeted the poor, however. Peter Brown argues that Christianity was able to exploit this oversight and build a strong base of popular support by giving charitably to the lowest levels of the urban poor, who had previously had too little status to get on the official public doles. This loyal following enabled bishops to expand their social power during the fourth century, helping to cement the church's new dominance in Roman urban settings by the fifth century. And, during this shift, more and more philanthropic giving became directed toward and administered through the church.
P. Brown, Power and Persuasion, and P. brown, Theough the Eye of a Needle are two excellent books to read if you want to learn more.