They should go through character creation as normal, though either of your first two bullet points will be fine
I've never run a Hunter game, but have a fair bit of experience with Vampire: the Masquerade which is relevant to this issue. My textual support, specific to preludes, is the prelude section of the VtM 20th Anniversary core rulebook (pages 352-354). Other points refer to the character creation process overall.
The Rules: character creation happens before the prelude, or in the absence of a prelude
1. Character creation does not reference preludes at all
You get the full range of options, including flagrantly supernatural ones not available to regular people, to spend your points on during character creation. I have never seen a rule restricting, nor suggesting restrictions, to mundane choices only (except in the case of a mundane character).
Particularly noteworthy is that characters are created before the prelude is played, and so if they want to purchase supernatural traits they'll have to do so before the prelude. At the same time, this ends up being functionally equivalent to your second option-- the prelude is intended to cover the time before characters are subsumed in the intrigues of the World of Darkness, and so they won't have access to any supernatural abilities during that section.
Additionally, character creation explicitly allows for (and almost demands) that players buy at least some supernatural traits. Things like freebie points flat out do not apply after that step, and point costs for traits exist to balance characters abilities for the game (to the extent that WoD is ever balanced...). Using their full point allotments for only mundane things and then getting supernatural traits for free, as in the third bullet point, doesn't suit this at all.
2. Preludes are not mandatory
They are strongly recommended, by White Wolf and by me. But you don't have to use them, and if you're going to start in the middle of the action anyways you don't really have to justify, through play, how and why your stats are what they are.
3. Preludes are about character depth and immersion more than game mechanics
The prelude section of the VtM book is heavy on emphasis that the prelude is a narrative device and is not intended to take all that much table time. It is not a special case of ordinary play-- characters do not earn experience, do not progress by purchasing additional dots, etc.
My Experience: preludes immerse players and emphasize how different the World of Darkness is from ordinary life
Preludes are too short to include much development of characters or situations, are much too short to make mechanical progress, and are fundamentally deterministic. Critically, characters are mundane during the prelude, and are (usually) very much not mundane in the chronicle proper.
Preludes are meant to cover one session, at most, for each PC. That isn't enough time for them to engage in lots of dice rolling or explore a plot in much depth. The outcome is already known-- the character survives the prelude and is a Hunter by its end or soon after. A prelude which uses a lot of specific trait ratings is already off target.
They work much more naturally to explain what the in-game stakes are for a character, why they think the way that they do, and how being drawn into the World of Darkness has shattered their previous normalcy. At the opening of your chronicle proper, your players' characters will be Hunters, and the character sheets they have indicate what they want their Hunter characters to be like. The prelude should explain how that transition comes about and dramatize what that means to them.
With those in mind, I submit that there is no difference between the first two bullet points in your question. Buying the supernatural traits is about what the Hunter is like, but before the prelude is over the character isn't a Hunter, and so they can't draw on anything Hunter-specific at that time. But mundane-only until the end of the prelude, then buying Hunter traits, suits character progression just fine. And during the prelude there shouldn't be enough scope for one character to be stronger or weaker than another in any meaningful way. In either case, the character build should come out the same way with the same overall point cost.