Paraguay face co-hosts the United States in their opening Group D match on Friday, marking the South Americans' first World Cup appearance since 2010.
"In my view, they have already won," Alfaro said of his players at a pre-match news conference on the eve of the game.
"After 16 years, they qualified when it seemed impossible, when there was no hope."
The Argentine added that the team had restored the connection with the fans: "They've recovered Paraguay's DNA."
While acknowledging the emotion surrounding Paraguay's return, Alfaro stressed that his squad's ambitions extend beyond merely taking part.
"We are not here just to be part of the World Cup," he said. "We're here to compete."
Alfaro expected the opening test to be difficult, with the United States playing on home soil under coach Mauricio Pochettino.
"Of course, it is complex to face one of the hosts," Alfaro said, pointing to the quality of their opponents' European-based players.
Paraguay would need to show concentration and discipline, he added, especially against a US side who were dangerous from set pieces.
Paraguay also received encouraging signs regarding the fitness of Strasbourg winger Julio Enciso, who is recovering from an injury suffered shortly before the tournament.
"Julio is doing very well," Alfaro said, adding that he had followed the required steps in his recovery and would continue to be assessed before a decision is made on his availability.
Alfaro said the squad, and the country, wanted Enciso to be ready, and suggested he would start if fit.
As anticipation builds ahead of Paraguay's long-awaited return to the World Cup, Alfaro said he had urged his players to stay calm as they counted down the final hours before kick-off.
"We waited 16 years," he said. "We can wait one more day."
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The 2026 World Cup will be held from June 11th to July 19th in the United States, Canada and Mexico. The tournament will feature 48 national teams and will be played in 16 modern stadiums.
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