Interesting thing I discovered for myself about five years ago. I have always been able to listen to a few bars of a song and know I liked it. (not all songs, and not all the time.)
Some songs, I just instantly knew. Well, it behooved me (as a songwriter) to figure out logically what it was I was attracted to, instead of just calling it "instinct."
Turned out (after about three months of probing my own mind) that there were two criteria that a song had to have in order to have that "instant like."
1. Had to "feel familiar" while being original. (That seems like what you are describing.)
2. It had to go in a surprising direction fairly early in the song to distinguish it from feeling too familiar.
The surprising direction could be musical, lyrical, or
?? But there had to be a surprise.
I always try to include a "familiar feeling" AND a surprise direction. Sometimes it seems to work for me.