tosac

 Enterprise: The First Adventure by Vonda N. McIntyre
James T. Kirk is the youngest man to be promoted to the rank of captain in Federation history. His crew consists of a first officer who finds him impetuous; a chief engineer who finds him arrogent; a chief medical officer who finds him trifling; and a helmsman who wants a transfer.

But the young crew, which would later become the legendary space explorers, quickly puts aside their differences when a monstrous starship appears on their nascent flight path.