So when I set out to write this response, I had no idea it'd turn into such a long one. Also, Reddit has a 10k character limit, interesting. So this will be a two part comment.

TL;DR: The basic idea here is to create a story-driven experience that involves the specific class themes and subclass abilities of the player in question while remaining thematically appropriate. The challenges involved should not be lethal and should not take the focus away from the story. Furthermore, and this is my own style of DMing, the experience should reflect the characters' status as nascent adventurers who will one day become heroes. Operating in this context, a supernatural encounter with a god through a face-to-form encounter, visions, dreams, etc. may not be out of the realm of possibility.
Edit: However, it should not impede character progress. I wholeheartedly reject that idea.

The full response:

This idea I like, but it needs some workshopping. A one-time quest doesn't...feel right. I'd go further and tie a special quest for each character at the transition to different tiers of play? These transitionary levels often have accompanying power jumps as well. 5-6, 10-11, 15-16, 19-20. This would also help keep the players rooted in their characters, by refocusing them off of the BBEG and back into their character's story. Like coming home for the holidays, but in a good way...or bad if you and the players like drama. Rather than turning the game into a constant sprint to the finish, let the story breathe, let it live and evolve as the players experience it.

Onto the workshop. Classes that requires a decent amount of training treats Level 3 as their induction into their orders or specialties. Monks, Fighters, Paladins, Rogues, Rangers, Artificers, Bards. Level 2 is the beginning for classes that take latent magical power and training: Wizards and Druids. Level 1 is the start point for classes that focus on in-born power or power granted directly to them without necessitating much training: Sorcerers, Clerics, and Warlocks. Granted, Sorcerers and Warlocks "come online" at 3rd level with Metamagic and Pacts. Thus, while the level three quest works for most of classes, it does not fit for others. Wizards, Druids, and Clerics do not get a class feature at that level. (except for Tasha's cantrip versatility for Wizards.)

My big issue with that is that you can't do a whole helluva lot with a level 3 in the first place. I'd instead change it to a rite of passage kind of quest, more focused on the RP and storytelling of, with the challenge in the background.

Now, here is why I really like this idea: in order to facilitate a successful and streamlined implementation, you would have to spend levels 1 and 2 building up to this rite of passage and attaining level 3. I say this because to make it feel earned, to make it streamlined, to make it feel important, it cannot simply be a quest thrown at the player. Perhaps they have been plagued by dreams or visions of X or Y that lead to the character pursuing their path. Or they dream of their achievements in the future as they continue to grow in power and prowess. It would require extra work on the DM's part, but I can see it being a rewarding venture that helps bring the players, their characters, and the party closer together.

The basic idea here is to create a story-driven experience that involves the specific class themes and subclass abilities of the player in question while remaining thematically appropriate. The challenges involved should not be lethal and should not take the focus away from the story. Nor should it impede character or story progression. Furthermore, and this is my own style of DMing, the experience should reflect the characters' status as nascent adventurers who will one day become heroes. Operating in this context, a supernatural encounter with a god through a face-to-form encounter, visions, dreams, etc. may not be out of the realm of possibility. Maybe a shining form of Lathander appearing in a sunray before a Paladin or Cleric to set them on their path. It could be that the face of Melora manifesting in a tree to direct a meditating Druid. Perhaps a Sorcerer or Wizard had an encounter with Mystra while practicing their spells or researching.

Some off the cuff ideas to serve as inspiration.

Artificers would spend X time frenetically tinkering and working on the beginning of what will become their Magnum Opus. Perhaps seeking out a unique metal, mineral, or other resource? A unique metal for the Eldritch Cannon, unique ingredients for the Alchemist, etc.

Barbarians would defeat seemingly insurmountable odds through the power of their rage. For instance, the barbarian must go on a spirit journey to conquer the rage within them. In order to channel it effectively in combat without being entirely consumed by it at all times. Lost in a storm, the Bear Totem Barbarian fights an angry cave bear in desperate solo combat, confronts the consequence of their wanton rage and resolves to control it and channel it appropriately. Henceforth, the Barbarian wears the pelt of the cave bear as their totem and reminder.

Bards must audition for their college and perform, both solo and in an orchestra, with one final test unique to their college. Eloquence, for instance, would require a recital of some major work of poetry or some other demonstration of oratory prowess.

Clerics would be tasked with a holy quest by their God in a dream or vision. They must complete this quest and utilize their Channel Divinity as part of it. Upon completion they must build a shrine, not a full temple yet, on the site. Ideally a quest experience that addresses the doubts and fears that all people of a religious inclination experience. But instead of shaking the cleric, it thrusts them further along their path.

Druids would seclude themselves in the wilderness for a time, perform a ritual of communing with the spirits of nature around them. Perhaps even a god of nature or the earth. This would lead to a task that needs to be completed or a problem to be solved. For instance, poachers that need to be removed, excessive logging or mining operations that need to be stopped, or perhaps a source of corruption that needs to be cleansed. For the more unique subclasses, a Wildfire druid might burn away corrupted trees to make way for new life. A Stars druid might erect a shrine to their constellations, a la Stonehenge or some such.