~ Sometime after Season 3 ~
The American side of Hero Society doesn't often get in the spotlight. Especially in comparison to their Japanese counterpart. The crime rate isn't nearly as low as Japan's, and the hero society isn't nearly as well set up. While a Hero License is required in Japan, in America it is not. Pro Hero isn't a career choice, it's more traditional where anyone with the strong enough drive or power can be one. In America the fact of 'Secret Identities' have stifled the rise of agencies.
It takes dedication and sacrifice to be a hero. Those who have quirks in America aren't forced to become heroes, but there is a glamour to the whole affair. There are some who can't afford to have costumes made or aren't willing to live a double life. Plenty of opportunities to do good outside of costumed heroism exist in America.
After Toshinori's retirement as All-Might, the world was looking for a new symbol to look towards. Bursting onto the scene is a hero that is being called the 'American All-Might'.
Seemingly indestructible, faster than a speeding bullet! Stronger than a locomotive! SUPERMAN has arrived! Soon, America's crime rate is closing in on Japan's record lows. There were of course already veteran heroes, but none seem to shine brightly as the Man of Steel.
After an interview with Lois Lane published in the Daily Planet, Superman is revealed to not be a quirk-user at all! He is in fact an alien who is the sole survivor of a far off planet called Krypton. To some this is world-shattering, answering the 'are we alone in the universe' question! But to most: the fact that a humanoid alien would risk everything to protect people fills the population with a sense of hope they haven't felt since the Kamino ward incident.
There is one person who is disgusted and filled with hatred for the hero. Lex Luthor, CEO of LexCorp and certainly not a super-fan. The Daily Planet had been looking for the scoop to bring Luthor's corruption to light for years. It seems they got their lucky break when a bumbling young reporter named Clark Kent and the efforts of Superman exposed LexCorp's seedy dealings. Weapons trafficking, corruption, money laundering and illegal human experimentation.
Lex wouldn't likely see a week of jail time, he promptly threw everyone else under the bus. But the public image of LexCorp and Luthor's facade of humanitarian and philanthropy were destroyed. Lex Luthor hated to admit it, but he needed some assistance. He heard about a group of villains in Japan on the run...what was their name? Ah yes, the League of Villains.
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TLDR; - Lex Luthor makes a deal with the League of Villains and recruits other local villains to help each other out. Superman and other DC heroes team up with U.A. and local heroes to try to foil their plot.