"all songs were new once"

But they weren't folk songs when they were new, they were just new songs. It takes time and process to turn a new song into a folk song. That needn't take very long, if the song touches a nerve with enough people and there's a mechanism for it to be taken up and shared. On the other hand, some very old and very well-known songs aren't 'folk'.

What makes it difficult now for a new song to become a folk song is twofold. Firstly, there isn't the same environment of people singing songs to entertain themselves and others - that's been taken over by readily available and portable professional entertainment. Secondly, where songs do enter the popular imagination there is nearly always a definitive 'correct' version to refer back to, so the variation which is an essential element of folk song is much less likely to occur. It's not impossible though.

A new song is just a new song. It may be 'folk', or it may be something else, and that may depend as much on the background and performance choices of its composer as it is to depend on anything inherent in its structure. it might be both, if it can be performed as well in one genre as another.