Gočmanac started training at the local Kopaonik Brus.[2] From there, he moved to OFK Beograd,[3] and after spending a year at that club,[4] in the summer of 2017, he joined the youth team of Partizan.[5] After another year, he was transferred to Teleoptik, and later signed a scholarship contract with the club.[6][7][8] The following year, he signed a professional contract,[9] and thereafter, he was a regular goalkeeper in the cadet category.[10]
Partizan
He joined the first team training in early February 2021,[11] and for the first time, he was on the roster for a match against Novi Pazar in the 21st round of the Serbian SuperLiga.[12] By the end of the season, he was on the bench a few more times and regularly played for the youth team.[13] After that, he was loaned to Teleoptik, where he spent two seasons and played in the Serbian League Belgrade.[14] During this time, he occasionally trained with the first team.[15]
Mačva Šabac
In 2023, he joined Mačva Šabac, signing a one-year contract with an option for an additional season.[16][17] He became a regular in the team at the start of the 2023–24 season in the Serbian First League.[18]
Vojvodina
In mid-February 2024, Gočmanac signed a contract with Vojvodina,[19] but according to the agreement, he remained on loan at Mačva until the end of the season.[20] According to Sport Klub, the transfer fee was estimated at approximately five million dinars, with ten percent of the next transfer included.[21] He reported to the coach of the Novi Sad club, Božidar Bandović, at the beginning of preparations for the 2024–25 Serbian SuperLiga season.[22]