D&D 5e idea starting as nothing.
Starting a campaign as zero-level characters has been around for the game's entire history -- it's just something they never established firmly enough to put in the core rulebooks.
For 5E, I'm seeing several gaming blogs that suggest simply starting characters with their race and background -- and only that. Establish a few traits (one Personality, the Ideal, and the Flaw), and you get a +1 proficiency bonus (given that you'll have few proficiencies). 1d4 hit points. Start with negative XP, enough for a couple minor encounters, say –75 or so.
Once they reach 0 XP, they get to pick up their chosen class and get all the benefits.