Goodman Games

Choose race and class like normal. Characters only gain skill proficiencies, weapon proficiencies, Armor proficiencies, and cantrips from their class. They start with half of max hit points plus con bonus. They gain all benefits from backgrounds. They start at -300xp.

That would be my take on it. Easy-peezy.

How about
Random race and Random background. Stats rolled 3d6 in order. d6 hit points. A roll on the trinkets table. -300 XP.

At 1st level reroll HP for your class and take the highest of current HP or just rolled HP.

I wrote an article about 5th Edition 0-level characters a couple of years ago. Sadly, I never got to use the idea.

http://bernietheflumph.blogspot.com/201 ... level.html