The defender was the toast of the tiny nation when his 94th-minute stunner sealed a 2-1 win over Senegal last week, but the amateur can generally be seen playing in front of a few hundred fans for Spanish fourth division side Langreo.
Alvarez's father is from Equatorial Guinea and the 27-year-old, who was born and raised in Spain, believes it is still not too late for his exploits to earn a professional contract.
"I don't need to earn millions and millions of euros, I would just be happy to have a professional contract and play football for a living," Alvarez, who goes under the footballing name of Kily, told Reuters.
"My dream is to play in England but I would be happy to go anywhere."
Alvarez comes from the opposite end of Spain's football spectrum to the millionaire players from clubs such as Real Madrid and Barcelona.
"Football can be a very tough, ungratifying profession," he said. "To be successful, a lot of things have to fall into place and you need a coach who has confidence in you."
Alvarez spent two years with Atletico Madrid's B team and was on the verge of breaking into the first XI when disaster struck.
"I was picked to play for Atletico Madrid's first team but the day before the match, I suffered ruptured ankle ligaments. Somebody fell awkwardly on top of me and that was that. It took weeks for me to recover and, by then, my chance had gone."
"It's a huge difference," he said. "Usually, I play in front of 600 or 700 people. In Bata, we were playing in front of 40,000 with the whole country behind us."
"I didn't know anything about Africa before that, I had no real concept of what it was like," said Alvarez, whose international career has taken him to impoverished and war-torn countries within the region.
"You do see things which affect you deeply. In Sierra Leone and Liberia we saw amputees, people living in very tough conditions. It's a shock and very moving but it's not like that everywhere.
"But many people have the wrong idea of Africa, they think it's all natives with spears and arrows, that everyone is dying of starvation.
"Of course, there is a lot of poverty but there's much more to it than that."
