Werewolf: the Forsaken
Being a Werewolf seems to be an all-or-nothing state. You've either undergone the First Change or you haven't. Prior to that, the character was probably Wolf-Blooded, but I don't know if that is always true. Blood of the Wolf has a chapter specifically about the Wolf-Blooded where it offers a sort of sliding scale of "wolf-bloodedness."
Now, my understanding is that werewolves, from the moment they're born, have a sort of hybrid spirit-soul. The opening story in Werewolf is about a pack that detects a guy is about to change, so we know that there must be something that can be detected. Were it me, I would tell the story of how the character sensed internal changes. Maybe they notice their moods change abruptly with the phases of the moon or that some familiar places now have an almost-palpable pulse and hunger to them. (You could signify these with a personality Flaw and Unseen Senses, respectively. Maybe let players reassign these dots later so they don't feel cheated if the Change makes them obsolete.) I would use these sort of scenes to highlight that they have always been different; there's always been something deep down that is now climbing to the surface. The First Change can come as a sudden shock or the external confirmation of what they had already begun to feel inside.
Changeling: The Lost
A human becomes a Changeling over the course of their Durance in Arcadia. Equinox Road p. 105-107 discuss the transformation and its 4 stages: mortal, enchanted mortal, fae-touched mortal, and changeling.
Basically, as a mortal interacts with Arcadian objects, they unwittingly make agreements with them -- By drinking Arcadian water, you agree that the water will quench your thirst. Over time, accepting these agreements allows the Wyrd to affect them more and more. Adapting to the land and their Keeper's demands is then what transforms them.
Since the transformation (as written) occurs while the character is a slave in Fairie and ceases to progress as soon as they leave there, I don't see this as a very viable way to portray a gradual change over the course of a story (unless you want to tell a story in Arcadia, which is what Equinox Road is kind of about). Of course, you could rule that the changes continue, even for those who were rescued or escape before they became full Changelings. This reinforces some of the hopelessness of the Changeling condition: A changeling, who fought so hard to rescue her brother from the True Fae, finds she can do nothing to save him from the infectious Wyrd.
Mage: the Awakening
If you've read Mage, you already know about Sleepers, Sleepwalkers and the Awakened. But Mage p. 334 mentions Proximi, people who have been touched by the Supernal. They're fleshed out much more fully in The Silver Ladder which gives rules for Proximus Dynasties. The Dynasty rules don't require a character to come from a mystical lineage necessarily; Dynasties are really just a set of Blessings (30-dots of themed rotes they can learn) and a Curse (which is roughly as severe and obscure as a rank 3-4 spirit's ban). On top of that, Proximi can use Imbued Items, hold 5 Mana, do Pattern Restoration and a couple other mini-mage things. If they Awaken, they keep the Curse but any Blessings become true rotes which they can cast even if they lack the Arcana.
So you could have a character who develops some intuitive knacks (Blessings) and from there begins to uncover family secrets (Curse). Or maybe they meet a mystical teacher who teaches them amazing things (Blessings) but explains that this path has a strict requirement or grave cost (Curse). Perhaps a truck full of liquid tass spills on them while they were walking down the street, and now they're experiencing peculiar side-effects (Blessings & Curse). From there, the characters could continue as Proximi, learning Blessings while avoiding the Curse, or they might Awaken. Since Curses persist and are fairly harsh, I'd probably try to give players opportunities to grab some non-Path rotes before Awakening.
Regarding Other Supernatural Templates
Mummies I know next to nothing about. Prometheans and Demons were never mortal, so there's no way to transition into being supernatural (if fact, Prometheans are trying to become mortals). Sin-Eaters might start as Gatekeepers, mortals who can open gates to the Underworld (Book of the Dead p. 50-51), though that's not really implied as a direct progression and Gatekeepers gain no other special powers, leaving a big gap between them and Sin-Eaters; probably not what you're looking for.
Now Vampires, however, have Ghouls (Vampire: the Requiem p. 166-168) and Larvae (Night Horrors: The Wicked Dead p. 100-115). Larvae are mindless minions that result from a botched Embrace. They can be Elevated into full Kindred later, but the progression from mortal to frenzy incarnate to vampire is probably not what you want since the player would lose control of the character during the larval phase. Ghouls, on the other hand, provide an excellent transition state (almost as perfect as Proximi). Ghouls can learn vampiric Disciplines and carry these over if Embraced, along with blood addiction and Vinculum. Therein lie the downsides: all ghouls need vampire blood, vampire blood is addicting, and drinking from the same vampire 3 times forms a Vinculum (a supernatural emotional dependence). If a player wants to have a ghoul character, they'll need to work out where the blood is coming from and what strings are attached (because there's bound to be some conditions). Additionally, when the time comes to become a full member of the Kindred, there needs to be a very good reason for a vampire to Embrace the ghoul.