An Academy product taken by the Sydney Swans with pick 32 in the 2020 national draft, Gulden announced himself with 3 goals on debut in Round 1, 2021. His 2023 season brought All-Australian selection, the Bob Skilton Medal and fourth place in the Brownlow count, and the 175cm midfielder returned from a pre-season ankle injury in 2025 to average 26.6 disposals. He has played 115 AFL games and kicked 79 goals.