Mexico begins a process with Cesar Luis Menotti, the Argentinian coach that won it all in 1978, in 1990. Menotti would become the architect of Mexico's development as the so-so football nation we know today. Mexico gets back in action in 1991 for the first edition of the Gold Cup. Still rusty, they lose the final to the USA. Mexico would then win in 1993 and bribe CONMEBOL higher ups with rolexes so Mexico could be a guest for Copa America and Mexican teams could compete in Copa Libertadores and Copa Sudamericana. This begins a golden age for el Tri, as they manage to reach 2 Copa America finals (1993 and 2001) and three third places (1997, 1999 and 2007) as a national team and three different Mexican teams reach the Libertadores final (Cruz Azul in 2001, Guadalajara in 2010 and Tigres in 2017. The latter would go on to reach the final of the Club World Cup) and Pachuca became the only team to ever win a tournament outside of its won confederation with the Copa Sudamericana of 2006. Here's the reason why Mexicans believe themselves to be "only below Brazil and Argentina in the Americas".
Beginning in United States 1994, Mexico would begin a streak of qualifying to every World Cup and attracted one of the most dedicated fanbases in the world. They also began a streak of always going out during the Round of 16. Mexico managed to see some remarkable players down this stretch: Hugo Sanchez, pentapichichi, during his twilight years; Rafael Marquez, a solid complement to Carles Puyol in Barcelona during the early Guardiola era; Jorge Campos, one of the finest goalkeepers of his era and borderline positionless striker; Cuautemoc Blanco, as talented as he was butt ugly and almost drowned in a pool. Among many, many others.
Mexico's streak was a textbook rollercoaster. USA '94, they are group leaders and lose in PKs to Bulgaria. France '98, another solid performance were they were eliminated by Germany, 2-1. Mexico got to host the Confederation Cup in 1999, and they managed to win it against Brazil. This is by a country mile still the greatest accomplishment they have.
On the way to Korea-Japan '02, they almost didn't make it. They sucked so they called Javier Aguirre, at that point the most accomplished Mexican coach and arguably, still today. He managed to drag Mexico to the World Cup, where they somehow won the group and then they were ruthlessly eliminated by the USA, 2-0, while the yanks were still figuring out what the fuck is a soccer. "DOS A CERO" became it's own meme on CONCACAF to reflect that a nation that barely gave a fuck about the sport was still capable of cucking Mexico out of things.
In 2005, Mexico managed to win the U-17 World Cup. For Germany '06, they had a legit solid team with a lot guys with European experience. Based on recency bias, there were reasons to believe Mexico could finally join the big boy table of football. Then Argentina showed up and while Argentina may not be very good at having a stable economy, they are very good at football. And specially, at making Mexico feel inferior. If Mexico was Johnny Joestar, Argentina is Diego Brando with the US as Funny Valentine. They never are able to beat them and how Mexico was eliminated in 2006, planted the seeds of a resentful one-sided feud with a country that up until 2022 was carrying itself with a stigma of futility. A legit canon event for a generation of beaners. Mexico would then experience the infamous collapse in the 2008 Pre-Olympic in Carson where they manage to land every shot on the one Haitian defending.