The relatively short answer is that the Aksum Kingdom (a precursor to Ethiopia) was not "cut off" from the rest of Christianity when it became Christian. There were already merchants and others travelling to and from Aksum in the early 4th century, spreading trade and ideas including Christianity. And note that this is the same time period as the rule of Constantine, the first Roman Emperor to adopt Christianity.

A lot of the credit for Aksum's rapid acceptance of/conversion to Christianity is given to (Saint) Frumentius and his brother Edesius, who was a Christian from Tyre but enslaved and given to the king of Aksum, then freed but they remained at court to tutor the soon-to-be King Ezana. Edesius eventually returned to Tyre, while Frumentius visited the Patriarch at Alexandria, was made a Bishop by the Patriarch, returned to Aksum, and continued spreading Christianity including convincing King Ezana himself to convert. Much like was happening at the same time in the Roman Empire, having the King/Emperor convert to Christianity was a big boon for widespread conversion across the rest of the kingdom/empire, and Ezana converting made Christianity the official state religion thenceforth.

So the conversion to Christianity in ancient Ethiopia was not at all some isolated event happening in a pocket of land surrounded by other religions, without connection to the rest of Christianity. Aksum had many trade routes and connections with the Roman Empire as well as other nearby states like the Himyarite Kingdom. It was well-connected with its neighbours and through them, plus access to the Indian Ocean, and through these Aksum was fully connected to the rest of the ancient world, too. Aksum's exposure and acceptance of Christianity came through these connections, as was happening in many other parts of the world.