Although da Costa's father was a Jew, the children of his second marriage were brought up as members of the Church of England.
In July 1840, da Costa emigrated to the newly settled colony of South Australia, becoming a successful merchant on Hindley Street.
He was elected to the committee of the Merchant's Institute, and became good friends with the colonial chaplain, James Farrell, and Bishop Augustus Short.
In his will, da Costa bequeathed his South Australian landholdings to St Peter's College, Adelaide.
The estate was subject to the life interests of ten relations; the last died in 1910 upon which time the property was vested in the school.