Actually, this came up a while ago in a discussion about TAW Exaltation criteria. Technically, if you look at the Bull, Dace, Arianna, Swan, Panther - even Harmonious Jade - Solar Exaltations don't come after you've something amazing, they come at your time of greatest need and let you do something amazing. Exalting as a Solar allows you to overcome impossible challenges; called in the moment of a hero's greatest need of them. They choose people with the potential and drive to use their power to change the world, and grant them that power so that they can, at the point where they are most desperate for it.
Which is a bit more interesting and distinct than just "do something cool", tbh, and is a lot more meaningfully distinct from other types of Exaltation.
This pattern holds true in the Eclipse Castebook.
Rune had been seduced by a raksha, whom he invited into Whitewall. For this crime, he was exiled, forced to leave the city's walls in the stormy heart of winter. The Fair Folk was outside waiting for him, and tried to lure him from the safety of The Road. Rune resisted, but he knew he would inevitably die from the cold. So he threw himself at the fairy lord to die fighting. After the fairy's guards dragged him off and held him still for their master to murder him, Rune became an Eclipse and gained the protection of a Quill of Heaven's Diplomatic Immunity, which allowed him to barter for safe passage to the next, faraway settlement.
Rhianna was trying to save a god-blooded horse from being put down by an owner who had lost too many trainers trying to break him. Answering the challenge to gentle the creature where no one else could, she told the proud stallion that this was as much for his good as hers. Even so and despite whatever respect he might have felt for her, he wouldn't submit to anyone who couldn't resist him, and he gave her the ride of her mortal life. She became an Eclipse Caste in order to survive, and learned that his name was Storm.
Mirror Flag was part of a troupe of actors who visited Great Forks, where they were arrested on charges of thievery. Flag took her Second Breath as she began to understand that the charges were true (her companions really were thieves) but also that there was a third party turning the enforcers of the city against them. The Sun himself spoke to Mirror Flag, telling her to tell her story and thus win her freedom.
Admiral Sand was an aging dandyman, a respected former business man and pillar of the community. He had removed himself from business and governance, but one day too many pieces fell into place. Snatches of conversation, rumors, market prices... he walked out into his city and marveled at how impoverished it had become. He barged into the city hall and demanded to know what his successors were doing, and their boasts and transparent lies sickened him. The Sun spoke to him as he took his Second Breath, charging Sand to become the bridge that brings people together. Presumably, the "danger" to which Sand was subjected was how close he had come to having his city and retirement and people come to utter ruin at the hands of mismanagement, leaving them all vulnerable to the depredations of rivals, bandits, and monsters.
In the Twilight book, Sayn was Exalted at his forge, as he hammered metal into a ploughshare and prayed to the Sun for deliverance from the drought that was killing his people.
Fehim was a redhanded criminal trying to escape the burning and sacking of his crime family's stronghold. Hanging off a third-story window over a sheer drop with nothing soft to land on, he let go to fall just as a guard struck him in the face with a club. If he had not Exalted, landing on his shoulder and head would have killed him instantly.
Horakinis had left her family behind to seek out knowledge which would let her restore order to humanity and the world, banishing sickness and keeping Chaos at bay. After many false trails, she was at the end of her resources and hope, knowing she would soon be forced to return to her home and become an accountant. She Exalted just outside of a hidden treasure-trove of books, following a trail that responded to her anima banner.
Iay Selak-Amu was a thaumaturge who came to an island to complete its shrine with a blessing to protect the village and its people from the Wyld Sea. He was too late; the Sea had already erased all creatures on the island, and all of the raw elemental substance left was slowly transforming into water. Still, he tried to enact the ritual, to name the island and keep the Wyld Sea from encroaching closer to his own home, but the island vanished into the Sea before he could finish. He managed to make it back into his boat, but any remaining land was too far away. Had he not taken his Second Breath, he would have died of thirst, hunger and exposure. Oddly, it was not the Sun who appeared before him, but a vision of himself.