I'm not any kind of expert on the bottomless abyss of White Wolf PnP lore, but having played the first Bloodlines, the "starting as a thin-blood" thing doesn't sound like a big deal. I don't think one needs some sort of fancy vampire-cannabalism explanation for it either.
Chapter 1: Play as a lowly thin-blood using the generic powers.
Chapter 2: Find out you have hidden talents; a screen pops up and you choose what sort of vampire bit you in the intro. You then demonstrate your lineage to whatever clan you chose and are accepted as a bottom-tier member, receiving training in using your new powers and working your way up the Skinner Box.
It's been confirmed the PC starts as a Thin-Blood and gets to (optional?) pick a Clan later, so presumably Diablerie is involved.
The hidden talent thing is a different sort of thing. There isn't exactly a precedent for that sort of thing beyond having a low enough Generation, but that actually isn't that important anymore because of the (smart) introduction of Blood Potency so Generation is not so pivotally important anymore (the Bloodlines PC was basically like every other VtM PC because they had lowest Generation possible; V5 removes the Generation background option entirely). HOWEVER! This is not to say there isn't some sort of hidden talent thing beyond just being regularly worthy of being a PC. A sort of buried concept in VtM was that of Inceptor, basically a vampire that has the ability to create NEW disciplines (as in, not learn new, but create an entirely new discipline on their own). Normally this is a rare thing that has happened with low Generation exceptions, usually Bloodline founders, in example Baron Samedi, the founder of the Samedi bloodline, is/was a 5th Generation Cappadocian.
But, the exception to this rule was/is thin-blooded Caitiff (as said, this is an old thing that's basically been dropped to limbo and never really elaborated on or formalized, so everyone takes Generation Five-Dot) can ALSO create all-new disciplines. But this is more of an esoteric and probably not going to be even considered thing since I doubt even Hagen and the other old edgemasters remember this thing.
What often confuses people is the difference between Caitiff and Thin-bloods. Caitiff are (usually) full-blooded Vampires with equal potential, but are left Clanless and without knowledge of Kindred society for various reasons. Thin-bloods are the Vampire equivalents of people with severe genetic defects.
Well there's never really been any real explanation for how the Caitiff thing works (and it only raises further questions because certain Clans aren't exactly something you need to be told about to notice, in general Clan weaknesses being a curse rather than a psychosomatic thing makes this a whole can of worms that has just been avoided), and it's made further confusing because until V5 there were occasions where Caitiff/Panders and Thin-Bloods were treated interchangeably, and before V5 there actually wasn't anything stopping Thin-Bloods from being part of a Clan. V5 drew a line in the sand in this regards, and provided by far the most comprehensive look at Thin-Bloods so far.
I mean, look at the PC in Bloodlines; he goes from being a totally useless fledgling to hyperpowered Vampire T-800 hosing down the Sheriff
Yeah, but that was already bending the lore quite a lot (which several pointed out at the time) and there was the untold implication that your "sire" was some hot shit in terms of blood lineage, which made you abnormally full of potential.
You definitely weren't a thinblood, and in fact even as the newborn in town you were sent to deal with a bunch of them and you were supposed to be the boogeyman by their standards.
I have personally never liked this criticism of Bloodlines' handling of PC progression being somehow against how it should be (almost as much as I despise nerdwords like 'lore'). It is, I feel, a very myopic and literal reading of how XP is handled in VtM and WoD in general, and one that makes makes categorical one-size-fits-all assumptions of things like genre, tone, and entire stories. That's actually one thing where White Wolf always did a poor job with, the XP explanation in Revised Edition and V20 is staggering in how long it is for something that's basically just handwringing about details over what's really a very simple thing. This is one thing V5 improves at, since the XP segment is a single paragraph and is followed by The Golden Rule. Now, I have a lot of issues with Storyteller's XP system (well, I don't think there isn't a single XP system that I don't have axe to grind with), like I don't like how it instructs to give XP after every session (I feel this actively undermines pacing), but it should only be seen as a tool and a fairly intuitive tool at that (unlike the living nightmare that is d20 experience points), but that's all it is and should be seen as: A tool for handling character growth and change within a story and inside the context of a game.
The best way to look at it in Bloodlines is that it's nothing to do with the character's Generation or anything of the sort. It's just that the PC gets shit done so they get better at getting shit done. If you look at it further, it also makes further sense because LaCroix is a pansy who has others do everything for him, which is why he's a complete pushover after his goons get mowed down by the massively bionic, hardcore, two-fisted yojimbo million dollar movie gangsta. And it's necessary for the story. Or alternatively, it's a video game, and it's more enjoyable if you don't raise each trait a single time over its entire course. Like, these aren't real things, nobody can actually objectively establish how long it takes for a vampire to git gud.