I figure it works something like this:
Rogers enlists as a soldier in order to take part in the test.
He is the only success, and the test is over.
He is, naturally, then sent to basic training.
By the end of his enlisted training, Phillips realizes Rogers is something special.
Phillips has a idea of how to use Rogers so he arranges a direct commission.
He then sends Rogers to Infantry officer and Intelligence officer training.
From there, the FBI academy.
Yes the FBI has a tradition of providing training to other agencys.