Born in Cadiz, Moncayo began competitive racing at a young age and won his first championship at the age of eleven, winning the Valencian minimoto championship before winning the championship of Andalucia the following season. Moncayo then moved up to 125cc level in 2005, competing in the Catalonian championship, where he would finish eleventh in the 2005 championship and improved to finish runner-up in 2006. He moved up to the CEV Buckler 125GP series in 2007 where he would compete for three full seasons, ending up with the championship in 2009 with three victories at Valencia, Albacete and Catalunya.

Moncayo made his début in the 125cc World Championship in 2008, making a wildcard appearance at the Spanish Grand Prix, finishing 25th in the race. He made appearances in the three Spanish races and the Portuguese Grand Prix in 2009, but finished outside of the points in all four races.

Moncayo moved into the 125cc World Championship full-time ahead of the 2010 season, partnering Danny Webb at the Andalucia Cajasol team. A fifth place, and three further top ten finishes helped Moncayo to finish in 13th place in the final championship standings.

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