Kukk was born on 9 September 1870 in Ilmatsalu, Governorate of Livonia, in the Russian Empire.

Between 1902 and 1904 he was assistant priest of St John's Church in Saint Petersburg.

He also served as a military chaplain during the Estonian War of Independence.

Kukk was elected the first bishop of the Estonian Evangelical Lutheran Church on 12 September 1919.

He was consecrated by the Archbishop of Uppsala Nathan Söderblom at the Charles' Church, Tallinn on 5 June 1921.