By a stroke of ridiculous luck, I got a level one Luxray on Pokemon Go.
I don't think there's any way to share it sadly, but when there eventually is through the switch, I'd be up for adding it to the collection.
I also have a level 5 one that I obtained earlier.
I know it was a while ago, but there were some questions earlier in the thread about how you do this: it literally has to be the first action you take on a new account.
Spinning a stop or catching a Pokemon always gives enough XP to raise to level 2. After that it's impossible to get a level 1 egg. The level of an egg exactly matches your trainer level, there's no randomness to it. Fortunately this is calculated before you get the XP that comes from receiving the egg.
(Catching the first squirtle/charmander/bulbasaur does not count as an action, it's fully scripted and gives no XP).
Absol and Mawile recently became possible to get at level 1 (because they spawned in the wild for a week), leaving just a handful of things that can't be level 1 in Pokemon go:
Can only be obtained through crazy egg luck:
Nincada, Ninjask
Klink, Klang, Klinklang
Shinx, Luxio, Luxray
Can't be obtained at all:
Shedinja
Alolan Marowak
Alolan Raichu