He came from a sporting background, as his mother Julia del Río had competed internationally for Chile at the IAAF World Cross Country Championships. He began to train in distance running with his mother as his coach from a young age. Díaz made his international debut at the 2008 South American Youth Championships in Athletics, where he was ninth. He represented his country at the global level the year after, running in the heats at the 2009 World Youth Championships in Athletics. He returned to continental level at the 2010 South American Youth Championships in Athletics and had his first success, taking the 1500 m gold on home turf in Santiago de Chile. Another youth level medal came at the 2010 South American Cross Country Championships, where his fourth-place finish led Chile to the team bronze medals. He began to make progress in the under-20 category at the 2011 South American Junior Championships in Athletics, taking a bronze as the youngest 1500 m medallist as well as fourth in the 800 m.