On June 17, 1995, the big puncher González became the first Cuban boxer to challenge for a heavyweight world title when he fought WBO champion Riddick Bowe at MGM Grand Garden Arena in Las Vegas.

His highlights include: After an outstanding amateur career in Cuba, where he defeated the likes of Teofilo Stevenson, Tyrell Biggs, and Craig Payne, he defected during a Cuban Team event in Finland, in 1991.

His progress as a professional was severely hindered by González's refusal to co-operate with trainers or training, feeling as a top Cuban amateur there was nothing he could be taught.

In June 1995, after a heated build up, he fought hated arch rival Riddick Bowe in Las Vegas, for the WBO Heavyweight championship.

Gonzalez blew his chance of redemption, as Witherspoon used his superior skills and big power to take González apart, decking him twice and knocking him out in five rounds, issuing an even more complete defeat than Bowe had done.