A gaming thought experiment.

Players decide what their character looks like – just their bodily description – and nothing else. They are told the game is Pathfinder, and each given a blank character sheet. The setting is modern, but players do not known their character names, role, class, skills, or anything similar. Explain that their characters are similarly amnesiac – they know what society is like and who is president, but not the month, day, or their own histories.

Each character awakes in a dirty room, with a pair of pants and a surgical gown. Have players describe their pants, but the gowns are all identical.
Characters will obviously want their characters to get out of their rooms and do something. Doors are locked, the building they are in dingy and abandoned. As players try things (Knowledge checks to recognize thigns, Strength or Dex checks to force open doors or squeeze through tight spaces, and so on) have them roll d20s with no modifiers. Include some threat appropriate to the genre you want to run (see LOST, Persons of Interest, Phantom: Requiem for the Phantom, Cube, Cabin in the Woods, and similar fiction for an idea of what to use).

Whenever a character misses a check, ask it the player would like a reroll. If the player does, tell them to increase the relevant ability/skill by 1. So a failed Str check reroll results in the character’s Str going from 10 to 11. Make sure to have a variety of kinds of things to do (an NPC in the same circumstance encourages social as well as physical efforts). If a characters rolls a natural 20 on a check, that also results in an ability/skill increase.
When an ability/skill hits the highest level possible for the game level you want to run, stop giving reroll offers. (For ability scores you may want to keep track along with the player, so you know if they have hit the point-buy limit. Of simply things, and just let players hit a maximum of +8 total ability score bonus, with half their ability scores being odd and half even).

For bonus points, give characters options of equipment from time to time, but limit what they can take. For example in each character’s starting room is a tool kit, a medical kit, a revolver, an automatic pistol, a crowbar, a pair of shoes, a riot shield, a utility knife, a laptop, a journal with a pen, and a make-up kit. Each is connected to a panel on the wall, out of reach of the others. When one is removed, the rest are hit by flamethrowers and destroyed. Whatever the character chooses, the character is proficient with. (Choosing shoes could be light armor proficiency – a desire to have protection, or the Run feat, or any of a number of options).

As the first game progresses, periodically have players decide on things their characters remember. The character’s name, nationality, favorite meal, and so on.

By the end of the first session, the characters find whoever or whatever brought them together, and overcome it. Then they get their memories back, and between the first and second game create their full characters, but must keep anything determined during the first session.