I was booting and operating my father's Apple IIe at 4 by myself and I don't consider myself exceptional, but rather having experienced exceptional circumstances.
The year was 1985. Against his hierarchy decision, my father bought one for work under cover of some big carbon paper order (that was used a lot at the time, so it really did go unnoticed) and hid it at home.
Bundled with the computer were two floppies with games, one with a rabbit in a maze and the other I can't remember. He booted them for me a few times. Then one day as he was gone at the office, I booted the thing on the DOS floppy, inserted the rabbit game floppy and started the game. I was caught red-handed when he came back. Boy was he angry (what if I screwed up and destroyed weeks of work?). It's actually the first time I can remember being scolded. Later when he cooled down and realized I could actually get it, he briefly showed me more things like LOGO and BASIC, which I enjoyed a lot. He did not know much on the programming front (he was more of a MultiPlan and WordPerfect user) so I was on my own on that front. I remember creating chains of GOTO to generate infinite loops on purpose, and genuinely trying to understand and build very crude purposeless but exploratory programs. Yet at that age and completely by yourself you really can't do much.
Then, less than a year later the computer gained its due recognition and went at the office, at about the same time we moved far away. I was not to touch a computer again for eight long years.