Since personality type doesn't change, I've been reading on how an INTP may be as a child and early adolescent. Yes, I was born with a developmental delay, and diagnosed with disorders like ADHD and aspergers, so that could affect the cognitive process of an INTP (or any personality type for that matter).
As a kid (from what I remember) from ages 4-12:
-I was adventurous, but hated getting into trouble.
-I was pretty oversensitive (almost complete opposite now amazingly)
-I had trouble doing things on my own (mainly from ages 4-8)
-I was interested in making friends to an extent, but after a while I became more interested in myself, and even moreso, my interests; I sat in my room and watched TV and drew all kinds of shit (comic books, animations, etc.)
-Had very narrow interests (weather, dogs, etc.)
-Was always questioning everything
-Very hyperactive and emotional (likely a part of the developmental delay)
-Was independent to an extent
-I was easily distracted
This is all I remember; there could be much more, but the above as a whole is pretty fitting for my character; and I have drastically changed over the years (I also missed school for 3 years due to a very bad situation I was in during my early adolescenthood, which cognitively affected my developmental stages, long story).