These who are born with great magical powers they don't know how to control, I think, are usually feared by others. If Charisma is considered to be a social skill, then shouldn't it be almost impossible for such outcasts to socialize? Or if Charisma is viewed as a power of a personality, rather than just the abilities to deal with others, are all the sorcerers born with such power of presence and such strong spirit?

It is said that in some cases, sorcerers may gain their powers not because of their genes, but via some extraordinary event, leaving them blessed with inherent magic. In that case, do they gain their high Charisma after they gain their powers or this kind of events happen only to those with high Charisma?

I asked so I am planning to play as a peasant, transformed into a sorcerer by the contact with some Wild Magic.

Keep in mind that all you actually need to start is a 13 in charisma. Then wild magic is dangerous ( heck magic is dangerous - magic without control is deadly)  so your typical peasant dies when exposed to wild magic the PC is somehow able to tap the magic with the force of their personality allowing  them to control it enough to survive but finding that they are now tapped into the magic permanently but not in full control of it (ever if they become a wild magic sorceror). Having a higher charisma allows for better interaction with the magic and perhaps greater control over it.

Quote from Wi1dBi11 >>

Keep in mind that all you actually need to start is a 13 in charisma. 

 In 5th edition there is no minimum stat requirement for your base class. It's only if you want to multi-class that you have to meet the requirement for your subsequent class(es).

Charisma is how well you can force your will on the world around you. Say you were born with your powers. You would learn quickly that people feared this. So you would practice the Deception ability to prevent them from finding out the truth. But what if you were from a long line of respected sorcerers? Then you'd have been trained in Persuasion so that you could better lead others. 

So when does the sorcerer gain their high charisma? Before the game starts, sometime during his/her backstory is the best choice for mechanics. But if you want to choose to limit yourself for roleplay purposes, you can start with a low charisma and then build it up via ASIs. Make sure your fellow players are ok with this choice since it weakens the team mechanically. 

It's D&D. It's whatever you want to do that doesn't ruin the fun for everyone else. 

Yes you could start with a 3 charisma as a sorceror - but you would never be much good and playing that one as a part of a team wouldn’t be doing the team any good. So let me rephrase - to be anything close to an effective so error you need a charisma of at least 13. 

I think the OP is touching (perhaps inadvertently) upon one of the the weaknesses of 5e - Charisma covers a lot ground and doesn't give it much granularity.

Anyways, Sorcerors can certainly grow in power. In terms of the ones that inherited their power, they learn to master it as well as their power growing within them as they age. Similar can be said of those who get it by being exposed to magic, although why it is growing is more intuitive.

Regardless of how a Sorceror obtains their power, it can certainly grow. As far as unsocial Sorcerors go... I'm sure they exist. Mechanically, it's hard due to the way 5e works. You could put your proficiencies in non-Charismatic skills, like Arcana, Insight or Religion. That would make a small difference for a powerful Sorceror at the beginning (+5 instead of +7), but it would become more evident as you character progresses (potentially ending with +5 instead of +11). If that's not enough for you, you could ask you DM to have negative Proficiency Bonuses, you'd start with +3 and then get worse? Or just a flat negative modifier? They may even be willing to grant equivalent bonuses elsewhere, so take a -2 to Persuasion, and get a +2 to Acrobatics or something. You never know.

I think, to answer the OP, either of your options could work just fine. There’s no reason in the rules for the character’s charisma to be either inherent, or come along with whatever gave them their powers. Either way is perfectly viable. What’s important, rules-wise is where the scores are at the start of the campaign. Where they were the day before is the kind of story detail you work out with your DM.

Really, I'd say it's less Sorcerers in general and more PC tier Sorcerers who have particularly exceptional CHA. So like, if you're a typical 11 CHA everybeing and you manifest Sorcerer powers, you're not really able to expand on them. It takes the force of will that comes from a higher than average CHA to develop even just a level 1 array of powers from that potential.

Quote from Kaelharan >>

These who are born with great magical powers they don't know how to control, I think, are usually feared by others. If Charisma is considered to be a social skill, then shouldn't it be almost impossible for such outcasts to socialize? Or if Charisma is viewed as a power of a personality, rather than just the abilities to deal with others, are all the sorcerers born with such power of presence and such strong spirit?

It is said that in some cases, sorcerers may gain their powers not because of their genes, but via some extraordinary event, leaving them blessed with inherent magic. In that case, do they gain their high Charisma after they gain their powers or this kind of events happen only to those with high Charisma?

I asked so I am planning to play as a peasant, transformed into a sorcerer by the contact with some Wild Magic.

My interpretation of sorcery is that while your powers are innate, they don't show themselves until you age somewhat or have them triggered somehow. Honestly, I may be a bit like a superpower lore copycat, but I think it's cool that some people might be born with the potential for becoming a sorcerer, but that their powers may never be triggered.

The idea of a baby being born with Charisma 20 is honestly ridiculous to me, and D&D adventurers level up as they use their powers more and more. Due to this, I think it's also reasonable that sorcerers - from a young age and maybe even birth - start with a tiny bit of power and then get more spells and stuff as they practice, and they'll eventually reach level 1 or whatever level is appropriate for the start of the campaign.

If you become a sorcerer through an event in life, then that's a kind of weird and grey area for how the rules apply. Personally, I think you can choose either path: That your character was naturally charismatic before, or that their sudden contact with powerful magic infused them with charm and persuasion. Sorry if I'm rambling or have confused your questions, but I'm tired and basically you can pick whatever option for your sorcerer because A) There's not canon for this and B) It doesn't matter if there was because whatever makes the most sense to you and the rest of the table is fine because this literally doesn't effect mechanics at all.

Do you actually know any babies? If they didn't have the ability to force their will upon others, we'd have gone extinct long ago. They are the embodiment of charisma, and I'm saying this as a guy who no, does not want to look at my coworkers pictures of their baby.

The wonder is that sorcerers are actually able to retain it as they age.

Quote from scatterbraind >>

Do you actually know any babies? If they didn't have the ability to force their will upon others, we'd have gone extinct long ago. They are the embodiment of charisma, and I'm saying this as a guy who no, does not want to look at my coworkers pictures of their baby.

The wonder is that sorcerers are actually able to retain it as they age.

Fair, you make a good point. Though I do think that a baby will at least have disadvantage on their persuasion checks because they're trying to communicate to people when they don't speak common.