At the 2016 Summer Olympics in Rio de Janeiro, Baláž etched a historic mark for Slovakia as one of the country's first archers sent to the Olympic tournament, shooting only in the men's individual recurve. Baláž managed to fire off a score of 631 points, including 18 targets of a perfect ten, for the fifty-ninth spot against a field of 63 other archers in the qualifying round, before he faced his initial challenge against the eventual champion Ku Bon-chan of South Korea, abruptly ending his Olympic debut in a harsh 0–6 defeat.