I believe the first US Navy actually belonged to Benjamin Franklin. The French gave it to Ben, not the US government.
Franklin's Contributions to the American Revolution as a Diplomat in France
"The colonies indeed needed help of every description--men, money, equipment, ships, and all things to fight a successful war. The long years of enmity between France and Britain opened the way for the leadership of Franklin. And he was not only the man to exploit it, but also the reason for the acceptance of thirteen states as a recognized nation in the world of nations.
During his long career of service, we shall never know how many men sought commissions in the Revolution. But this much we do know--that Franklin was never deceived, as he never held out any hope for a commission unless the applicant had the ability in his chosen field. One of the men aided very early was John Paul Jones; and as an Admiral in the little American Navy composed of two ships under his command, he took those two ships and sailed into English waters for a fight. In a terrific battle, two proud English ships surrendered; and they were brought into French waters as American prizes."
I could not easily find confirmation of what I remember learning about the French giving Ben a Navy, but...
-Will