Barinaga started his career with Newell's Old Boys, before heading to Agrupación Deportiva Infantil Unión Rosario (also known for its acronym "ADIUR")[5] at the age of thirteen.[6][7] Following a 2016 trial, Barinaga joined Belgrano in early 2017.[8][6] He was moved into Alfredo Berti's senior set-up in mid-2019, originally as an unused substitute for a Copa Argentina loss to Real Pilar and a Primera B Nacional win over Barracas Central in July and August respectively.[2][8] Barinaga's professional debut would arrive on 6 September during a 1–1 draw on the road against Deportivo Morón, after he was substituted on in place of Sebastián Luna.[8] He scored his first goal on 5 December versus Independiente Rivadavia.[8][9][10]