Actually The Marines have been around LONGER than either the National Navy Or National Army.
The First Marines were recruited to serve on Privately owned Privateers even before the Continental Congress owned any ships. At that time the troops of the rebellion were composed entirely of of State militia rather than a national "Continental" Force.
The only US Military force that can trace it's lineage further back than the Marines is the National Guard, which dates back to the Massachusetts Militia of the 1600's