A friend of mine took me through a Dungeon Crawl Classics 0-level adventure last year and it was one of the most enjoyable role-playing experiences in recent years. I don't know how well it would work in 5e, but in the DCC module we had 3 players. Each player had four characters. Each character had a commoner job: carpenter, blacksmith, etc. They had some "equipment" that made sense for their background. The DM would allow us to prepare more equipment if it made sense. E.g., a farmer is likely to have a shovel, pitchfork, etc.
Basically, a member of the village found an entrance to a long-forgotten dungeon. When he disappeared and people came looking for him to make sure he was all right, they found the entrance dug in from his home. Some brave villagers put together a group to go find him.
Many/most died. But we had a great time.
Thinking about what made the DCC experience so fun, here is how I would do level 0 in 5e.
1. Make sure the players are on board.
Many players want to skip to 3rd or 5th level. Not everyone like low-tier play. Make sure that they understand that they will be playing multiple characters and most will die. Eventually, they will choose one to be the main adventuring character.
2. Start with 4 characters
Come up with a way to have 2-4 characters on one sheet of papers. They won't have much in terms of equipment or abilities, so it should be doable. Explain to the players that it is expected that some will die. From any that make it to first level, you'll choose your main adventuring character.
3. Build based on race and background--no class
I think the easiest thing in 5e is to first come up with the attributes as normal (whether rolling, point buy, or standard array doesn't matter).
Next, select a race and apply and stat changes, proficiencies, skills, and traits.
Third, select or make up a background. This will give them some additional proficiencies, skills, and equipment.
They should only have items granted by their background. They or their family or friends in the village may have other items they have access to, but they will not start with weapons (unless a soldier or similar background), and dungeoneer packs, etc.
Starting the Campaign
Easiest is to have them from the same village. Something comes up and they join a posse to hunt down a threat. A sink hole to a forgotten dungeon appears and a child falls in. They put together a group to save the child. This way they have acccess to items from their homes and other villagers. Allows them to realistically provision themselves with little money or starting equipment.
You could also have them all members of the caravan. Or part of a large group of refugees fleeing some war. But whatever the background, the odds are stacked against them so at least make sure they have some means to get basic equipment and provisions.
I'd milestone it. They either hit their first level and select a class after the first adventure or after a short series of adventures. I would say 1 to 3 sessions / 4-12 hours of play seems about right.