Kirk is just too seasoned for it to be his first command, but it is possible. I think writer's bible is pretty powerful evidence since Gene is the creator of the show, it's his show, his universe.
On the other hand, if you discount that, I can stil see Enterprise as Kirk's first command. You're talking about a freaking medal of honor recepient and a few other high awards (if he got them before Court Martial). If he has shown tremendous aptitude, why hold him back? Also, Kirk loves Enterprise a little too much. You don't get the impression that he would ever leave her, he's the loyal type - but if some destoroyer was his first command, why did he leave? More oportunities?
I tend to lean towards him heaving a command earlier, but it was so insignificant, that Enterprise is his first real command. He might have done a patrol or two before getting the new assignment. It was like an internship.
BTW, according to background info, Kirk was an ensign while at the academy, and as soon as he graduated, he was promoted to LT.