Early Settlement of Australia By 5tm Apr 27, 1770 Captain Cook Captain Cook first set foot on Australian soil on this day at Botany Bay. Jan 26, 1788 First Fleet On this day the first fleet arrived in Australia. It's now known as Australia Day. Period: Jan 26, 1788 to Jan 1, 1900 Great Southern Land Jan 5, 1802 Matthew Flinders Matthew Flinders explored Corio Bay and climbed the You Yangs