This is for D&D 5e, or any edition that contains the "Divine/Favored Soul" origin for the Sorcerer class. For reference, Sorcerers ("Sorcs" for short) are people who gain magic power from an inherent, internal source, rather than wielding it through the medium of spells and learning it through years of hard study. For them, it just... happens. Divine Souls are sorcerers whose power is legitimately divine in nature; they've got a piece of raw godhood in them, however small, and it lets them cast Divine spells just as well as Arcane.
My origin story: In whichever universe I'm playing in at the time, there was a deity who was "dispersed" (i.e., destroyed-but-not-quite; their essence is still floating around in the ether), long past most mortal memory; records of them might not even exist at all, anymore. One day, thousands of years later, a mortal is born whose soul, on its way to the plane to be incarnated in its body, becomes entwined with a strand of that deity's dispersed essence, where it becomes as essential a part of them as breathing. This essence is what gives this mortal access to Sorcerer abilities.
It also creates a deep, abiding wanderlust within them as they grow up; a desire to venture out, explore, and attempt to "reconnect" with other lost pieces of that deity's essence. This could be a fools' errand that would never truly see completion, or it could be a genuine possibility, perhaps consisting of lengthy trips into the Astral Plane to track down the rest of that deity. They'd have the power to do that themselves, certainly; but it would be far easier to do if they had a group of other adventurers behind them, helping them out, as well. Not to mention how the general nature of deities to gather people together under their cause and individual values would also play into their personality.
This opens up a number of possible plot-threads, as well. Because such a sorcerer could claim a direct, verifiable link to the divine, they can be seen as a threat by more established religions, or other gods who might not like the idea of a new god reconstituting themselves - although the flip side of the coin, other gods helping them to do so, is equally likely. And if this lost deity had any Angels, then any who've survived to the present day could still exist, either under the service of other deities or residing on the mortal plane as Fallen Angels. Maybe the deity's former personal Solar (their direct servant and most powerful Angel) could exist as well, attempting to do exactly the same thing as the sorcerer, and so is finally given renewed purpose once they actually meet.
Ancillary to the above idea: I have this running thought that, should the sorcerer succeed in obtaining more pieces of this dispersed deity's essence, this can lead to them gaining their own Paladins and/or Clerics; in effect, they bestow some of their power to other mortals, thus ensuring the sorcerer themselves doesn't become too strong because they are deferring to others. Imagine, say, this coming into play should the party's Fighter wish to convert their class levels to Paladin, and this becomes possible in RP terms once they found another "piece of divinity" to grant them that power straight from the very one they're traveling with.
Please comment & discuss. I'd like to develop this idea some more.