Hennadiy got his start in football at the FC Chornomorets Odesa youth school.
So far his longest playing stint has been with his home town team Chornomorets, which lasted 5 years.
In 2002 Altman, along with his father moved to FC Chornomorets Odesa and was battling for the starting position with Vitaliy Rudenko.
At the start of 2007, Altman left Ukraine to sign with Israeli club, Hakoah Maccabi Amidar/Ramat Gan where he would not count as a foreigner since he is Jewish.
After his father's unexpected firing in 2007 he was transferred to another Ukrainian First League club, PFC Olexandria.