Pucovski started playing cricket when he was quite young. With a tennis ball, his father, a cricketer, played with him at the time. Then he started representing Brighton Grammar in school cricket, and shortly after completing his education he joined the Melbourne Cricket Club.
Later, in 2015, he made his ODI debut under-19 for Australia. He has scored just seven points in his three ODI Under-19 matches (all against England Under-19).
After signing a contract with the Victorian Bushrangers, he started playing domestic cricket for Victoria in 2016. Pucovski went on to score 650 runs in eight innings in the 2016-17 National Under-19 Championships, including four consecutive hundreds for Victoria Metro.
Later on January 10, 2017, he started his A-list career by competing for Cricket Australia XI against Pakistanis. Before being caught by Hasan Ali, he scored ten points during the game.
