Are the starters shiny locked?

Been trying to get a shiny eevee by pressing F12 cause I heard thats the reset button for the past 5 days and still havent gotten it. I guess im really unlocky or have I been wasting my time trying to get it?

Nothing is shiny locked aside from the Mystery Gifts, so you’ll get it eventually, but you can get a shiny Eevee way easier via friend safari.

kind of want to get it for when starting off. trather do it like that and as soon as you replied and saw the reply, I skipped the shiny eevee so rip me. time for the grind again.