Jorge Luis Pinto's men are tipped to make a swift exit from Brazil after being drawn against Italy, Uruguay and England in Group D.
But Gonzalez is hoping Costa Rica can exceed expectations just like they did at the 1990 World Cup in Italy, where they progressed to the round of 16 alongside Brazil before they were eventually beaten by Czechoslovakia.
"This is the 'group of death'. No-one's under any illusions about that," the Columbus Crew defender told FIFA.com. "Our three opponents are all big teams and they've all won the World Cup before.
"But like we said, this is a whole new story. We are going to give it our very best shot, and we're excited at the prospect of doing well in Brazil and doing our country proud.
"I know my team-mates and how much work we're putting in. I'm confident in my qualities and those of the team as a whole.
"We're going to give everything to make the next round. That's what we want to do: make history.
"Italy 1990 was the only time we've managed it, but this team knows all about setting and achieving goals."
Gonzalez also believes the gap in class is now closing throughout the world, pointing to Costa Rica's results during qualifying in CONCACAF as an example.
Costa Rica defeated powerhouses the United States and Mexico en route to finishing second in the standings.
"The feeling I get is that there's not such a big difference between teams any more, not just in the CONCACAF Zone, but in general, around the world," he said.
"You get some very close score lines now. The USA and Mexico used to qualify easily, but that just doesn't happen now.
"This time around Costa Rica qualified in second place and Mexico struggled, all because the standard is higher now."
Costa Rica face the Republic of Ireland in an international friendly on Friday before opening their World Cup campaign against Uruguay on June 14.
