[2] He earned a silver medal in the men's rifle prone at the 2003 Pan American Games in Santo Domingo, Dominican Republic, and also represented his nation Cuba at the 2004 Summer Olympics.

[3][4] At the 2004 Summer Olympics in Athens, Estpinan qualified for the Cuban squad in the men's 50 m rifle prone by placing second from the Pan American Games.

[3] He scored 581 points to obtain a last spot out of forty-six shooters in the prelim stage, failing to advance further into the final.

[5] Estpinan also sought to compete for two more editions of the Olympic Games, but finished farther from the standings to achieve a qualifying place on the Cuban team.

At the 2014 Championship of the Americas Tournament (CAT) in Guadalajara, Mexico, Estpinan unleashed an astonishing target of 208.1 points to win a gold medal and secure an Olympic quota place for Cuba in men's rifle prone, hoping for his second Olympic bid after a twelve-year absence.