I recently came across what I think is an even earlier source, Gaelic Psalm singing, which was brought to the US and continued by what are called Old Regular Baptists.

This source accounts for the twanginess of country vocals more than what I've heard of Appalachian folk music, which is softer and more Irish.

Gaelic Psalm singing: https://youtu.be/_belSyGmVFk

Old Regular Baptists: https://youtu.be/5RejtoTc86c

And of course there are African influences (e.g. the banjo) and the African-American blues tradition, more commonly cited by early country performers than afterwards.