I am assuming that James does not know his birth name. If he did, he could look up his entry through Ellis Island. It is unlikely that someone coming from Spain would enter the U.S. from any other port, although quite a large number came through the Port of New Orleans. Louisiana is a predominantly Catholic state. Perhaps you should be looking for a Catholic Charities Orphanage in Louisiana.
If you were to look up the local Catholic Charities office nearest you, the director there could tell you the name of the archives for Catholic Charities which I have forgotten, but it's in Illinois, I believe. Something like Palatine, Ill. I forget exactly.
The director can tell you the names and locations of Catholic Orphanages in existence for the time frame you are seeking.
He may even have more information.
I am 60 years old. I was in a Catholic Orphanage. They had me there, and I had already found the Orphanage and its records. I was seeking information on the Orphanage, which I received, along with some pictures which recalled memories even though I was quite young. Like the Sisters of Charitiy's coronets. I remembered them exactly.