Well, you did learn to understand German sentences way before school and grammar, I think that was the point. A baby can learn any language without studying its grammar, and in the early period not being able to pronounce the words.
Learning the first language as a baby takes many years - and even after these years, you are still only on a "baby talk level". That is why I don't consider these "natural" approaches for learning a language to be a good idea - they are far too slow to be economical.