Early in his career, Dubina competed with Anna Adashkevich on the junior level. They placed 13th at the 1996 World Junior Figure Skating Championships. Following that partnership, he teamed up with Elena Kokhanevich, with whom he placed 12th at the 1998 World Junior Figure Skating Championships. He then teamed up with Anna Kaverzina and began competing for Russia. They won the bronze medal at the 1998–1999 ISU Junior Grand Prix event in China and placed 8th at the 1999 Russian Figure Skating Championships.