When did the Lutheran Church ministries start?

It is uncertain what the question means, but the Lutheran church began in Australia with the arrival of the first group of German settlers escaping from persecution of King Friedrich Wilhelm in Prussia.

21 German Lutheran refugees arrived on the ship 'Bengalee' on 18 November 1838, followed two days later by the main group on the 'Prince George'. They first settled at the town of Klemzig in South Australia.