Barreiro began his career as a player in the lower categories of Escola Basket Xiria de Carballo (La Coruña) and later in CB Sant-Yago. In the 2010 Minicopa ACB he became known to the general public, playing as a guest for DKV Joventut. In the 2011 Spanish Youth Championship, he averaged 18.1 points and 9.6 rebounds in 25.1 minutes, which attracted the attention of several Spanish clubs. Later,
FC Barcelona invited him to play in the 2011 Minicopa ACB and the UBSA Youth Tournament. In September 2012, Barreiro joined the Real Madrid Basketball youth team, in the cadet category. His first campaign in the white team was marked by his great performances with the cadet team but also by his numerous minutes with the Junior team, reaching the Ciutat de L’Hospitalet NIJT Junior Tournament. In this prestigious tournament his numbers, being a younger player, were: 5.4 points, 3 rebounds and 1.2 assists per game. In the 2013–14 season, Barreiro joined the Real Madrid Basketball Junior team, where he combined his participation with the
Real Madrid B Liga EBA matches. He started the season by winning and being named MVP in the Villaviciosa de Odón Junior Tournament, thanks in large part to his performance in the final: 23 points, 8 rebounds and a PIR of 28 in 24 minutes. In January 2014, Real Madrid Junior won the Ciutat de L’Hospitalet NIJT Junior Tournament, a championship that the white team had not won since 2006. On 13 April 2014, they were proclaimed champions of the Madrid Junior Championship by defeating Tuenti Móvil Estudiantes A and Espacio Torrelodones A in the Final Phase. On 10 May 2014, Real Madrid won the 2014 Spanish Junior Championship, held in Marín (Pontevedra), after 14 years without winning in this competition. ==Professional career==