In 1849 Genko entered the elementary school of Tukums, then the grammar school of Mittau (now Yelgava), then studied at the Saint Petersburg Institute of Forestry and Surveying, from which he graduated in 1862 as second lieutenant of the Forest Administration.
In 1880 Genko returned to forestry activities as a junior scientist forester of the Imperial Estates Administration where there was less bureaucracy and red tape.