All songs nowadays considered "folk songs" were written by somebody, and usually much more recently than the romantics suppose. Many can be traced to their original writers.

The first appearance in print of a song noted from oral tradition only tells us that it wasn't made after that date. The first appearance of a broadside text, however, can be one of two things: the first surviving example (whether re-written or copied from an earlier print form or -again, rather less often than people used to think- adapted from oral sources); or the original.

Sometimes, broadsides derive from earlier, oral forms; but that isn't something that anyone should take for granted. Frequently they don't.

Note that I'm talking of texts here. Tunes are more complicated on the whole. Sometimes, though, these too can be traced to an identifiable composer.

Really, the only problem is that many people come to the subject having only heard one example of a song; typically a recorded arrangement made by their favourite professional performer. As a result, they are likely to assume that there is only one form of it, and that there must, de facto, be "sheet music" or "chords" to be got; and that it is entirely unnecessary for them to tell us anything at all about the song they want information on. Presumably, from their point of view, we must already know all that. After all, they do.

Modern songs are another matter entirely, of course.