A lot players make Exalted character normal people with Exaltation thrust upon them. One day they are thinking about how they are going to get their crops to give a good yeild and then BAM! they can level a stone house with a punch. It may take a few sessions before they even realize that they are gods incarnate.Try to have the character's choice of destiny be an organic one. Tie into what each character values and then expand that to epic proportions. Does he want to have power, then world domination could be his epic goal. Offer him chances to take power of small communities and little by little he will be the ruler of a nation Does he seek knowledge then tempt him with the secrets of the Abyss and the Sidreals. Whatever the case, make sure that the characters have a core passion that drives them, and build from that.

When I played Exalted, my character gradually awoke to his destiny through gameplay, paticularily his Exaltation. My character started as a strapping farm boy with no desire than to work the Earth, make friends, get a wife, and one day have a farm of his own. Then his Exaltation occured and everyone in his small community became terrified of him including his own mother and father. A pariah, my character was determined not to become the monster everyone claimed he was and swore never to take a life. After a couple of session my character wound up in a small trading town, where his kind was tolerated. After a couple more advensures the towns people began to appreciate and look up the character and his companions. For the first time since he was run out of his homeland he had been accepted. That is when my character choose his destiny to restore Solar Exalts to the status of heroes across the world. When I made that decision, it felt right, and it dictated how my character acted from that point on.

I'm not familiar with Solar Exalted, but it sounds like the characters are very powerful.  Well, to make it interesting, there must be conflict.  Instead of asking them what to do, come up with enemies and events that will challenge them -- at that level of scope.  Does an enemy want to supernova a character's home solar system as revenge?  -- or if you're an evil GM, start it off with the supernova when they're on planet.  Does a despot want to enslave all 100 kingdoms and has already enslaved 23?  Is there some weird disease affecting whole races or robbing them of their powers?

I'll have to agree with Michael, most Exalted, especially those who have recently exalted are more likely to retain their original motivations for a little time and that's just fine for the story. For example; your character that wants to explore the Hundred Kingdoms, he's basically a walking plot hook and will (hopefully) keep the circle moving, but once he's been to much of the Hundred Kingdoms (which can take years in game, people forget just how big Creation is) or found some sort of travel artifact, then he is perfectly free to expand his motivation to "Explore all of Creation" or, if he knows they exist, "Explore all the Celestial Directions".
Heck your Character that wants to overthrow the Despot allows you to through into contrast what happens when a country's leader, even a bad one, is removed. This can even lead to discovering the Usurpation and the truth behind why it was done. This character could then justifiably begin to "Understand the Fall of the First Age" or maybe just "Conquer the Blessed Isle" if they're a Dawn.
Not every character can or even should start with "Restore the Veneration of the Unconquered Sun" or "Forge the West into one Nation" (lots of water very hard to hold together, also Leviathan, lintha pirates, angry Raksha, and so on.)