I just read your new entry on "free play" and it seems wise - esp. when you discover that what appears to be random notes may actually be discovery of patterns.
I first had a keyboard: a little electronic organ, then a piano - when I was a child. I had no lessons, and in that sense missed out. But I did explore. With the organ I was given a little book meant for adult learners I now realize. When it introduced intervals, I played around with intervals, finding what I loved and hated. The organ had a kind of vibrato through its reeds and for some reason it produced the sweetest M6. I got different instruments - a mouth organ, a descant recorder - and I would explore sensations, sounds, and invent music which later I found out actually had classical structure. It was the sandbox metaphor. For 35 years I had no piano, and I was nearly 50 before I had my first lessons on any instrument. When I finally asked for music theory, the intervals I had explored as a child, mostly nameless, had meaning and emotion for me - they were not just numbers to be memorized.