One could say that the source of Catholic social teaching starts long before the promulgation of Rerum Novarum. See the Gospels, the Acts of the Apostles, or the Epistles. But as far as non-Scriptural sources go, I’d pick St Augustine of Hippo’s City of God as the first Christian teaching to address the question of the well-ordered society, and the contribution that Christians can make to the common good.
You’ll find a succinct summary of this massive work here on Sparknotes, and a book by book summary here on New Advent. The City of God was written as a response to the accusation by pagans that all of Rome’s problems at the time were the fault of the Christians (sound familiar?). St Augustine first points out that pagan society carried within itself the seeds of its own destruction, and then goes on to show that although Christians are citizens of the City of God (a heavenly City), as “resident aliens” in the City of Man during their earthly lives, they can and should contribute to the common good of the society in which they live.
I’ve written a bit previously about this work, here where I summarize the introduction to the Image edition by Etienne Gilson, the French historian of philosophy and a Neo-Thomist philosopher in his own right. Here I go on to comment on what Gilson had to say.
Augustine’s City of God is a timeless work relevant in any age, for the City of Man will always be looking for a scapegoat on which to pile blame for its own problems. Certainly that is the case these days.