Item 1.
A far, far more successful Thomas the Apostle would be a good start - converts a minor prince. Said prince goes onto converting his court and neighbors... then you have small area that is Christian inside the melting pot of - Hindu / Buddhist.
Item 2.
But Egypt being Coptic Christian would be also a good start.
Item 3 - ASB version.
There has been some question of what was Jesus doing before he did his ministry - if you go in the Gospel accounts there is almost nothing for almost 30 years. (Yes, there are books that have been deleted, but I am talking about the official canon books) One of the most outlandish theories is Jesus took the show on the road and visited other countries - after all his profession was carpenter / mason / prophet? - the proposition being that Jesus went to India and became Buddhist, brought the Buddhist message back, and due to mistranslated of the message and executive meddling by the Apostles and (later) Bishops Christianity came into existence.... and therefore Christianity is a unknowing heresy on Buddhism.
If we go with this theory where Christianity is a Buddhist heresy -> India is the home of the Buddha.