Báez came through Argentina's youth structures, representing the Pumas Under 19 team in 2008 and the Under 20 side a year later at the 2009 IRB Junior World Championship. He later went on to turn out for the Argentina Jaguars and was a member of the Pampas XV team that competed in the 2012 and 2013 Vodacom Cup competitions in South Africa as well as their tour of Australia in 2014.