I'm surprised anyone would think that Enterprise was probably Kirk's first command, or that anyone would prefer to think that.
It's not that big of a stretch, given all the other more outlandish things that happens in Trek. A young command division officer distinguishes himself as a leader multiple times on various missions as he moves quickly up the chain of command. Upon reaching command rank, Starfleet gives him the Enterprise
. For all we know, a senior admiral of his acquaintance may have recommended him or even wrote the orders for him to take command.