No, you cannot get the shiny version of Cosmog or any of its evolutions, Cosmoem, Lunala, and Solgaleo, in Pokemon GO.
Cosmog and its evolutions are still relatively new additions to Pokemon GO, having debuted in late 2022, so Niantic has not added the shiny versions of the game yet.
Despite this, there is finally a way to get a second Cosmog in Pokemon GO, which means you can finally add both Lunala and Solgaleo to your Pokedex!
Is There a Shiny Cosmog, Solgaleo & Lunala Release Date?
Niantic has not announced the release date for the shiny Cosmog family, including Solgaleo and Lunala, yet. Unfortunately, it looks like it will be quite a while longer before these shinies come to the game.
Usually, Niantic releases the shiny version of Pokemon one year after they initially release, but Cosmog’s release has been very different to other Legendaries.
Despite being Legendary, the way to get Cosmog, through a Special Research Story, is much more like a Mythical Pokemon. As it usually takes many years for a Mythical Pokemon to get a shiny version in Pokemon GO, we don’t expect to see shiny Cosmog, Lunala, or Solgaleo any time soon.

Shiny Cosmog
Shiny Cosmog is nearly identical to the standard version of the Pokemon. The only difference is that the circles on its cheeks are red instead of blue.

Shiny Cosmoem
The shiny version of Cosmoem is also very similar to the standard version of this Pokemon, but the difference is more noticeable.
Shiny Cosmoem has a pink central orb instead of blue.

Shiny Solgaleo
Shiny Solgaleo is bright red with purple markings on its body. This is a radical change from the white and orange normal version of this Pokemon.
However, shiny Solgaleo retains the golden and galaxy colors around its face and mane.

Shiny Lunala
Shiny Lunala has an extremely cool dark red and purple color scheme, but keeps the golden wing edges from the standard version.

Hopefully we will see shiny Cosmog and the rest of the shiny Cosmog family in Pokemon GO soon. We will update this article if Niantic reveals when they are coming to the game!