One group I played with some years ago, back in 2nd edition, had, as part of their character generation/background process, an explanation of what event caused that character to gain the experience points that pushed them from 0th level to 1st level.

For example the Ranger I played in that campaign was a country farmhand who grabbed an axe and successfully killed a couple of desperate goblin raiders who came to plunder the fields.

I really liked this idea, and am mulling using it again in a 5e campaign I've got planned for the autumn. But I wondered whether there was any official rules material to give rigour to this process.

So: is there anything in 5e rules and supplements that describes the process by which an ordinary 0th level person becomes a 1st level anything?

(This was inspired by this question, which I thought was asking the same thing)

There is no 0th level

D&D 5e expects players to start at level 1. NPCs don't have player class levels, so there's never such a thing as a 0th level character. A NPC fighter doesn't actually have fighter levels, he just has a stat block that incorparates some fighter skills into it.

Because there is no such thing as a 0th level character, there are no rules on how characters gained their first level, because that's how they started the game. How you wish to fluff your character becoming a ranger however is up to you. It might be related to the background you've picked, but it might not be. "I used to be a merchant, but now I'm a fighter because I defended my town from goblins" is a perfectly valid explanation. The rules don't care either way, they just care that you've made a level 1 character.

That would most likely be covered by your background. You might be a fighter because you used to be a guard or a gladiator. You might be a druid because you used to be a hermit. You might be a cleric because you used to be an acolyte.

As part of the character generation process you are generally expected to come up with a backstory featuring the background of your character and how they became who they now are.

As mentioned in other answers, the background would cover this. To play it through though, here is an example of how my DM in one campaign handled it.

They had us write up our backstories and then give it to them ahead of time. Then one-on-one would role play specific events in our backstory. All rolls where done using a straight d20 with no modifiers to signify an average person, prior to their adventuring of developing different skills. That also means you don't really need a character sheet at this point and could leave things like your class more open ended.

An example would be that I wrote that my character was left for dead after defending their sibling from an attack that ultimately killed the sibling. In role playing it however, my character managed to stand their ground for longer than I had envisioned before being taken down but upon recovering rolled so poorly was unable to determine what became of the sibling. Now, there is a chance of finding out the fate of the sibling whereas the story I wrote had already determined their fate, turning that part of the story from one of revenge to one of looking for answers.

Now having said that, you would want to have good trust and communication between DM and players to do this since events could unfold differently but everyone in my group seemed to really enjoy how our characters developed by doing it this way.

No official books have guidance for "level 0" characters

The Player's Handbook assumes that when create a character at its lowest level, you begin at first level. How you effectively got your first level depends on your Background and the story you created for it. The rules offer many ways on how to flesh a story before the adventure, but none of it encompasses the "0th to 1st level step" in a mechanical sense.

However, an Adventurer's League module has guidance for it

The DDAL-ELW00 - What's Past is Prologue module written for the Embers of the Last War storyline has some guidelines for it, including the following:

A level 0 character has 6 + their Constitution modifier for hit points, 1d6 hit die, and no proficiency bonus. Weapon and armor proficiencies may be granted by race and background; those are fine!

If you care to look to an alternate system for inspiration, Dungeon Crawl Classics has a new character option that I think was called a character funnel. You essentially generated a bunch of level 0 peasants (there were numerous tables to randomly determine the peasants background), then had them get caught up in a significant event, and those that survived gained level 1 and turned into PCs.

The one time I participated in such a game ended up being a lot of fun. Each player started with 5 peasants of various occupations, then our village was raided, and in the course of the ensuing battle most of our peasants died. I think we ended up averaging about 2 survivors per player, from which we picked our PCs and determined our classes. For me, having the characters background and transition to an adventurer be played at the table greatly influenced how I evolved them as a character.

I have often thought about adapting this process to DnD, but I have never sat down an worked it out.