I've found that there usually is a moment in a programmers technical career where it just clicks. I find that what seems like productivity is almost always a direct result of a higher order of understanding.

An analogous situation is your average first year PhD candidate. Initially making some sort of contribution to the field feels overwhelming and almost impossible. But once you've spend a year or two reading papers and having coffee with the leaders in the field, everything comes together. That same PhD student starts to churn out quality papers every 6 months or so.

I think back to what it was like watching my dad program in Scheme when I was in high school. I got the same curious and overwhelming feeling then as I do now when working on certain areas of distributed systems. There's no reason to believe that the barriers that grownups face are any less insurmountable than the ones children do. :)