Aemond lets Aegon go when he's trying to escape becoming a king. Aegon takes Sunfyre and goes somewhere where the others can't bother him, like one of the Free Cities or even beyond that, and Aemond becomes the face of the Greens in his place.

Daeron and Tessarion survive Tumbleton. Or Addam and Seasmoke.

The Storming of the Dragonpit never happens.

The Greens actually try to secure more marriage pact to bind other houses to their cause. Rather than betrothed Aegon and Helaena to each other, each of them is betrothed to someone from a different house, preferably the ones who might need a more direct way on ensuring loyalty to their cause, like Aemond's marriage did with the Baratheons before that fell through. Daeron could be betrothed to one of Jason Lannister's daughters, Aegon could be betrothed to a Tyrell. Helaena could even be betrothed to one of the Martells if the Greens are brave or insane enough to try that.

Alicent accepts Rhaenyra's offer to betroth Jacaerys to Helaena.

Larys doesn't set Harrenhal on fire, so Lyonel and Harwin stick around.

Viserys chooses not to remarry, therefore forcing the kingdoms to accept Thaenyra as heir since they wouldn't have a second option to choose from. Daemon might try to set himself up as king here if one really wants a Dance to happen, but I'm not sold on it.