So breaking the Groundhog Day curse will be tough for the team known as El Tri, despite the fact they dominated their CONCACAF qualifying group and have posted some promising results in friendlies against tough opponents.
Coached by Colombian Juan Carlos Osorio, they have won 30, drawn eight and lost seven of his 45 games in charge. But some of those defeats have been traumatic -- notably a 7-0 massacre by Chile at the Copa America and a 4-1 loss to Germany in the Confederations Cup in Russia last year.
Osorio has faced frequent criticism in the national media, especially over his record of experimenting with dozens of different players -- a total of 66 to date.
The question is whether he has learned lessons from episodes like the German drubbing, and is getting closer to discovering his best team.
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There are signs that might be happening. In the past six months, the Mexicans have beaten Poland, Bosnia and Iceland in friendlies -- the last a 3-0 win against a side that made the quarter-finals of Euro 2016.
They held highly-ranked Belgium to a 3-3 draw in November, and spoiled their run of form only with a 1-0 loss to Croatia in late March.
Players to watch include spectacular goalkeeper Guillermo Ochoa, defender Hector Moreno and the attacking pair of Hirving Lozano, 22, and Javier 'Chicharito' Hernandez, 29.
Mexico's fans are also expected to present a colourful spectacle but they will have to watch their step.
World soccer's governing body FIFA last year warned Mexico over “insulting and discriminatory” chants by a small group of supporters during a 2-2 draw with Portugal at the Confederations Cup in Russia.
It had previously fined Mexico for fans’ homophobic chants during the side's World Cup qualifying games. Mexican players in 2016 launched their own campaign against homophobic slurs during matches.
(Reporting by Mark Trevelyan; Editing by Toby Davis)
