For the most part, becoming a sorcerer is impossible. You either already are one, generally by birth, or you never get to be.
Meaning it should not be possible to multiclass into sorcerer.
The exceptions where a person could become a sorcerer later in life are rare, and subclass restricted.
Most Sorcerers have some form of arcane awakening in their early life, but not all.
I'd suggest to look at it like a mutation in the Marvel comics. It might happen as a direct causality from something that has affected (or infected) you, but it might also happen due to changed environmental impulses (like walking into the Underdark with the Faerzress radiation, or walking into a region where the Shadowfell with it's shadow magic bleeds into the material plane, or having to endure multiple plane shifts within the span of just a few moments, one of which is literally a layer of hell) or just from enduring elevated levels of stress that activate some until then dormant features of your being.
At least that's the explanation I would go with if one of the players at my table decided to multiclass into Sorcerer.
After all, with 5e it's not possible to have a character just be two classes at once like it used to be in AD&D.
The only justifiable sorcerer multiclass I've noticed in this game would be the Aberrant Mind subclass, what with the tadpole.
Conversely, Draconic Bloodline should never be available to multiclass into.
The Draconic Bloodline is based on the old 3.x Prestige Class of Dragon Disciple, which made the character spontaneously sprout scales as soon as you became one, which couldn't happen until level 6 because you needed 8 points in Knowledge Arcana and your max rank in any skill was class level +3 for class skills, so you had to get to level 5 before you could even choose to become a Dragon Disciple.
Essentially your heritage either showed itself only at this point, or you had been changed into your new form by whoever made you a Dragon Disciple.
Multiclass into warlock should only be doable if you character actually meets and makes a pact with a patron entity in game, limiting subclass according to said patron.
And then the story would acknowledge the pact even if you respecced out of warlock, like I assume it does for Wyll.
Honestly, it is downright laughable that we can freely both respec and multclass into Warlock and Sorcerer, but can't start already being an Oathbreaker.
Don't get me wrong, I love that there's an actual mechanic in game for breaking your oath, that's a downright amazing inclusion.
But implying that your Tav already broke their oath before the game starting is much more reasonable than bypassing the implications sorcerer and warlock are supposed to have.
This is a slightly more reasonable argument, but I'd still opt for player happiness rather than forcing them to look for a magical creature that I have full control over when to make it appear... with how active these beings are in their search for new followers it wouldn't be completely out of question to have them appear in the middle of the night in a dream the character has and offer them a better chance at getting what they desire most.
Saving the biggest for last on purpose here:
Cleric subclass should be restricted by god. Or god by subclass, depending the order in which they are selected in the character creator.
The idea of people worshipping one god, but getting the power of a subclass that's basically the opposite, which that god either shouldn't be able to grant or would simply refrain from doing, feels about as ridiculous as being a 20 Str 8 Dex barbarian that exclusively uses bows.
I get the argument, and some combinations definitely feel weird, but I had players make some really great arguments for why they would choose a specific subclass in combination with a deity that doesn't seem to match on first glance, but made perfect sense from the point they were coming from.
And this is a CRPG adaptation after all... it's not like the players would be able to argue their case before their DM so that the latter can make an exception in that specific case... just offering the players a carte blanche so that they can decide on how they want to approach the logical implications of their decisions is a good decision in that case.
After all, you don't have to multiclass into any combination that you believe is unjustifiable.