It doesn't seem as though GOG users will be playing Metro Exodus in the near future.
The game is slated to come to Steam on February 15, but according to the official Metro Exodus Twitter account, it will not be released on GOG "in the immediate future."
When asked by a Twitter user if the game would eventually see a release on GOG, they received the following reply:
We have no current plans to launch Metro Exodus on GOG in the immediate future.
--- Metro Exodus (@MetroVideoGame) February 5, 2020
"Immediate future" doesn't necessarily mean it will never come to the service. Folks on the internet are speculating since it's a newer game, the fact that GOG is DRM-free may be the reason for its absence. That's just speculation, though so keep that in mind.
Previous games in the series, Metro: Last Light Redux and Metro 2033 Redux, are both available through GOG.
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If you are playing Metro Exodus, you should know the game's next DLC expansion, Sam's Story, releases on February 11. It is the second major expansion following The Two Colonels which released last year.
Also, if you are a Stadia Pro member, the game is free on the service this month.