I have a keen interest in the Nestorian Branch of the The Faith.
As the article indicates, the Faith was flourishing in China until the "Mohammedans" cut them off from the larger community. The world was pretty much Evangelized within a few hundred years after Christ's Death and Resurrection.
There is evidence that missionaries reached this hemisphere (New World) within a few hundred years.
Christian Designs Found In Tomb Stones Of Eastern Han Dynasty (86AD)