A large Greek minority? Please share your sources for that because I'd be very interested in reading that.
AFAIU, Greeks were there, but as traders who came because it was a prosperous kingdom. For the same reason other groups from around that region also had a presence, and vice-versa. Prosperous nations tend to exchange populations and build economic, cultural, and political ties.
But if you're implying the presence of Greeks or an adoption of Greek culture was the reason for the rise of the Aksum empire... I'd certainly like to read those sources.
The very early adoption of Christianity might have had something to do with it, at least in terms of creating a unifying identity within and among the broader region. But Greeks weren't the only Christians. Ethiopia already had ties to non-Greek Levante and non-Greek Arabian peninsula communities, and probably Persian traders, as well--Persians were the Greeks of the Indian Ocean. Not coincidentally, the Horn of Africa sits at the nexus of multiple major economic spheres and sea routes. The Aksum Empire originated in the highlands, but for much of their time they controlled or had a strong presence along the coast.