It has been a long time since I played Vampire, but - not only is it possible to do a group creation followed by individual preludes - it's the best way to do it.
You will probably need to have a gap in time between the creation session and the first Prelude. There will likely be some tailoring needed once you know the characters. But that's not a huge problem most of the time.
Character Creation for the Mechanics and the Meta
The Character Creation session should be used as a chance to have players become familiar with the system if they aren't already, and to discuss a few details of their characters to ensure they will work together and not have too much overlap.
You also have players discuss meta elements. Perhaps two players want to play rivals. They can discuss these details during this process, decide why they're going to be rivals.
Work up the full character, but I'd suggest telling players that no choices are final. Give them a chance to make changes once they better understand the mechanics and the setting.
During this part of the process, you needn't discuss more than the bare minimum of setting details. You know, just enough to make sure the characters will all fit within the premise. "You're all newly embraced kindred in the crazy world of high finance in the 1980s. Think American Psycho meets Vampire Diaries." Just enough to ensure the characters will work in your premise, and no more.
Prelude for the Setting and Story
Once you have the characters set, you can run individual preludes. This is the stage where you begin to introduce setting and story elements, and it can be run as free of mechanics as you and your players are comfortable with.
It need not be less interesting just because the characters are mortals. But making a story compelling does depend a lot on the GM. If you make the journey memorable, it will be awesome.
The last time I played Vampire, my GM did it this way. I built my Assamite, and then we roleplayed his journey from boy, to man, to trained assassin, right up to the scene where his mentor bites him on the neck and then hangs him up on a meathook. It was horrifying, and gut churning, but it was never dull. Along the way, my GM hinted at what it meant for the future.
You mentioned Initiations in Dogs in the Vineyard. As a GM, I've used this idea in preludes for other World of Darkness games (and other games) to help make them memorable. Players make characters, and then I ask them to ask a question we will answer during the prelude. This helps keep them engaged as they search for their answers.
This way will preserve nice balance between player agency and GM mystery. Players have freedom to create the characters they envision within the limits of the premise, but the GM doesn't reveal too many secrets too soon. I've played it, and run it, and it works well.
Your friend is correct that neonate is not the rank of a new Camarilla vampire; they're called fledglings.
However, the difference is merely legal-social — a fledgling is still the responsibility of their sire, with all the actions of the fledgling attributed to the sire. This keeps sires motivated to keep their childer in line and to teach them how to be functional members of vampire society.
Notably, there is no power difference — again, the distinction is only social (VtM20, p. 19):
A neonate is a young vampire, one who has not been Kindred very long. The main difference between a neonate and a fledgling is that the neonate has been emancipated from her sire and otherwise is seen as an “adult” in vampire society. The line between fledgling and neonate is incredibly subjective.
The stats of a fledgling vampire then would be the same as of a neonate. However, VtM is not a strict rules-as-written kind of game; when the Storyteller is doing something non-standard, the Storyteller is expected to make the necessary adjustments that make sense. In particular, you should decide which abilities on the PC's sheet require teaching, and not allow them to be used (or not used at full pip strength) by the fledgling until receiving that teaching from their sire.
Though this focuses on Camarilla, the fundamental nature of a fledgling doesn't change when you look at Sabbat — it's still a social distinction. A Sabbat fledgling may have a harder time learning their bloodline's abilities of course, but self-discovery is a good, if harsh, teacher and befits the situation of a shovelhead.
Best Answer
Age and Generation are assumed to be linked for character creation…
The fifth edition makes an explicit assumption that the members of a coterie will be of the same (or at least very close) generation; see under “Age and Generation” in the character creation section, on page 139:
For this reason the book doesn’t explicitly support what you’re asking: there’s no Merit or other equivalent to the Generation background of previous editions, or the ability to increase Blood Potency with bonus points as there is in Vampire: The Requiem.
(You can increase Blood Potency with experience points, but you only get XP at character creation if creating an older vampire who likely already has a higher Potency, and the three tiers presented - Childer, Neonate and Ancillae - either get too few XP to raise it, or only enough that they’d spend nearly all of it on one extra point. This wouldn’t change your generation in any case.)
Instead, the default idea is that you choose the age and generation (together) for the coterie as a whole, as per the character creation summary on page 137 (under “The Sea of Time”).
…but there’s no reason you can’t do this anyway.
The easiest answer - with Storyteller approval, of course - is to just give the character a lower generation (along with the corresponding minimum Blood Potency, and all the advantages and disadvantages that carries with it). The text on page 139 goes on to say:
And, as noted in the chapter on “The Blood”, on page 214 (at the end of the section on “Generation”):
So lore-wise you can definitely still have a lower generation freshly-Embraced Kindred. Just assign them the lower generation, without the additional experience points - those represent age and experience, not anything supernatural (as noted on page 151). With lower-generation vampires even rarer in V5 than previous editions, though, you’ll want to put some thought into why such a fledgling would be hanging out with other more common childer, and not being watched over by their sire or other more powerful vampires.
The main consideration from a balance perspective is long term. Blood Potency 2 is good, and will make a character more powerful, but that’s basically just 20 free XP. The much bigger advantage is that the character will be able to increase their Blood Potency beyond 3, assuming they live long enough and don’t mind spending a lot of their XP on the trait. But that brings its own problems - primarily, the character will have much more trouble slaking their hunger, and the severity of their Bane. (Note that errata released in the free V5 companion increases both the dice granted for a Blood Surge and the severity of Banes by one for all levels of Blood Potency, making high BP come with bigger drawbacks and rewards.)
If you want to balance this rules-wise somehow, I would first suggest limiting generation to no lower than 8, as in previous editions. That’ll minimise the impact of the above, and fits nicely in line with the limits of the old Background.
You could also use one or more of these suggestions, which I’ve based on systems I’ve used in other games (I’ve not tried this in V5):