Sotomayor was only 14 when he first cleared 2 meters (6' 6 3/4") and by the end of 1983 he had a best of 2.15 m. He then set the junior world record on 19 May 1984 by clearing 2.33 metres (7 feet 7 3/4 inches) at a meet held in Havana. He was not able to go to Los Angeles, California for the 1984 Olympics due to the boycott by Cuba (and most communist nations). In 1985 he took silver in the World Indoor Championships in Paris, with a best jump of 2.30 metres on 19 January, and then improved his personal best two months later outdoors in Havana, with a jump of 2.34 on 20 March 1985. He continued to improve the following year with a best jump of 2.36 m at a meet in Santiago de Cuba on 23 February 1986. He won his first international title in 1987, at the Pan American Games, and established a new personal best of 2.37 m (7 feet 9 1/2 inches) at a meet in Athens, Greece on 20 June 1987.