I think there is a common misconception that learning like a child will take 10 years to sound like a ten-year-old. I live in Japan and I can tell you that there are not many native English speaking foreigners that can speak Japanese as fluently as a six-year-old, let alone a ten-year-old. While either child may not know some words that a learner knows, the child knows many more words than the foreign learner and can speak with impressive fluency.
Yes, all children learn their first language naturally. Before they can start reading, they learn a vast amount of the language without looking up any words, and without asking questions. They certainly never take notes (because they can't write either.)
Is learning naturally, a slow way to learn? Some say that it takes the child 10 years to reach the level of a ten-year-old (which is actually a really impressive level if an adult finally reaches it) and so we as adults can learn much faster and shouldn't try learning naturally. I say to you, be aware of these types of arguments. For they are all false!
Let me tell you about a person from Korea who was adopted when he was eight-years-old. His adoptive parents didn't speak Korean, nor did his peers. So how did he learn English? The natural way! He had to experience everything and go through all the stages of natural learning. There simply was no other way. I met him when he was eighteen. By that time he had forgotten all of his Korean long long ago. And how was his English? It had been 10 years, so was he only at the level of a ten-year-old? No, he was way ahead. He was at the level of a young adult on his way to enter university.
I have no idea when he actually caught up to his peers. But it certainly illustrates to me the falseness of the argument above.