I realized that, even in my very different lines of work, I feel the same. Like Paul, I am now four years past completing my undergraduate studies, and within the last year I have felt more confident in my work. I credit it to accumulated experience as well as being trusted and empowered to take on greater challenges and responsibilities by my superiors.
I have had a number of people who in the context of being my boss have also served as professional mentors to one degree or another. They have continually encouraged me and challenged me, and I know that I am indebted to them for the professional success I have had to date. Having a tremendous education such as I received from Wheaton College was a huge foundation (apologies for the hyperbole, but anyone who knows me knows it is hard to resist when talking about Wheaton), but I know that my professional mentors were (and are) profoundly significant in my young professional years.
And so, for any more junior young professionals reading this, let me say two things. First, be patient with yourself if you feel that you have yet to "achieve" anything. And second, keep learning, and find professional mentors who can help you keep learning.