What if Meri died ten thousand years ago? (Sits down to watch the chaos that would have caused)
There are two possibilities here: Things happen as usual, but Meri doesn't take a cryopod, so she dies on Earth; or Meri and Blue never even make it to Earth. We'll start with the simpler one.
Meri makes it to Earth, hides Blue, then goes off and finds humans to live with for the next several hundred years until she dies. She builds a home there, and she ends up mostly happy, even if she spends the rest of her life waiting for Allura to show up with a new generation of paladins.
Things don’t change much for Voltron, because Meri actively kept herself from influencing Lance when he was a kid. It's on Earth that things fall apart, because Meri isn't there to get Akira out of the Garrison when Iverson calls for the assassination. Akira dies, and Karen and Eli follow soon after. (Iverson sent Val to Project Balmera because she was a nobody, but he’s freaked out at Karen and Eli’s visibility and probably wouldn’t take the chance if he could help it.)
Obviously the absence of four fairly major players has ramifications for the rest of the series, but it's just sort of... progressively more bleak... as Shiro, Hunk, Matt, and Pidge come home from war to dead family.... and then have to go off to fight again without a good chunk of their support system, including a paladin and at least one adjunct (more than that depending on which adjunct theories you subscribe to.)
SO! The other option. (Sorry in advance, cause this intrigues me and it got long fast.)
Meri dies on Altea, and Blue never makes it to Earth. Instead, Zarkon captures her, and he maintains control over both her and Red for the next ten thousand years. He tries to force both of them to take new pilots, but they refuse. In some ways, its easier on them to have each other, because they form a kind of spiritual bond that lets them lend each other strength. It's kind of like the bond between dual paladins, actually, and as soon as Zarkon realizes what they're doing he separates them, but at that point it's too late.
Red and Blue spend the next ten thousand years conspiring, searching the universe for their new paladins. And it's weird, because in this AU after Matt crash lands on Earth, he, Pidge, Hunk, and Lance have no way to get to space to join the fight. They go on the run and basically end up in hiding with Mama Holt's Army, fighting back against the Garrison and screwing up Iverson's efforts to keep the Galra from open invasion. (The Blue Lion isn't on Earth, no, but the Vkullor egg still is, so the Galra still took an interest in Earth and still discovered the way humans produce way more Quintessence than they should. So Earth's plot still works, just without the paladins flying off in Blue.)
Red and Blue in some ways kind of egg each other on, and having Blue there definitely makes Red a little less wary of the Galra she's noticed flitting about the edges of her awareness with a potential Black in tow. (Side note: this hasn't come up in Duality yet, but I consider it canon that Blue has a better sense for who the other lions might choose than any of the other lions. Which is to say, in Duality proper Red doesn't know that Shiro is a potential paladin, she just knows that Keith shows some promise. In this AU, thanks to her bond with Blue, Red instantly recognizes both Keith and Shiro as solid paladin candidates.)
So fairly early on--not immediately after Keith gets Shiro out of the Arena, but within a few weeks, once Shiro trusts Keith a little more--Red basically absconds with her two new children. Around the same time, Blue has chosen Nyma and Rolo as her paladins, probably because they brought in a bounty or sold some supplies on the ship where Blue is being held/a nearby planet where she could sense them. They're too wary and Blue's too well guarded to get them to come to her, so instead she sends Red to them, and then they stage a prison break for Blue.
So to start, you have Keith flying Red, Rolo and Nyma co-piloting Blue, and Shiro just kinda, "Okay, I guess this is an alien thing, then." Only once Blue's out do she and Red take their paladins to the castle-ship to awaken Allura and Coran. With one example of dual paladins already in front of her, Allura is more open to the sense she gets that Black wants both her and Shiro, so they start training together even as they all debate what to do about Green and Yellow. Allura confirms that both lions are still where Sa and Rukka left them, but they don't have spare paladins hanging around right now, and the Empire is already hunting them. Things aren't going well with only two lions in play.
They end up finding Shay and then Ryner, and the first time they form Voltron is during the liberation of Olkarion. They continue on from there, searching for Sam and Matt and fighting back against the empire for a few months. (It's somewhere in here that Matt gets sent back to Earth and that whole plot kicks off, degenerating fast until the Galra say screw it and start sending troops down despite Iverson’s protests.)
It's a very different team dynamic with the paladins because Shay and Keith are the only teens on the team, and everyone except Shay already has experience in battle. They function much more like a military unit, which puts a lot of pressure on Shay. A lot of pressure. Ryner very much takes her under her wing, as does Rolo, but she’s still struggling.
I'm not sure the exact circumstances under which this encounter would happen, but things come to a head when Haggar takes control of Shiro and immediately sends him to Earth to deal with the mounting rebellion courtesy of Mama Holt's Army.
In the interim, the paladins and their families have gone deep underground. Val didn't immediately get in on the investigation because Lance never went missing, but Akira.
Akira has just returned to the Garrison from a contract when the news breaks. Matt Holt is back, and he's alive. The Holts have already gone to ground, so Akira can't get in touch with them, but he knows that if Matt survived, then Takashi probably did, too. Akira presses just a little bit too hard and is quietly made to disappear into Project Balmera. (It's after this that Val begins her investigations, so she has a few brushes with death but doesn't end up captured before all-out war comes to Earth.)
Haggar arrives with Shiro, and that's how Shiro and Matt's reunion happens: with a mind-controlled Shiro trying to kill Matt's family. They fight, but Matt's still recovering from his captivity and sure as hell can't stand up to Shiro like this. The only reason he doesn't die is because the paladins followed Haggar here and Keith and Allura arrive in time to stop Shiro killing Matt.
The other humans get involved because they want to save Shiro, and at first there's more pushback from their parents (There's already a fully functional paladin team out there, Pidge, they don't need you!) but at the same time, Earth has effectively been at war for a few weeks now, and the paladins' families are in the thick of it, so it's a little bit easier to win the parents over. You end up with the same paladin team except that Rolo takes Meri's place in Blue. They save Shiro and Akira and it's pretty bleak for a while after that, but they eventually heal, and find their footing, and continue on with the war and the search for Sam.
Or if I'm feeling particularly evil, instead of getting rescued, Akira takes Rolo's place and winds up with Sam hahaha Don't kill me.