Is it possible to Do GoG giveaway

Not on this site, at least not via giveaways function

Mayoslice has [a giveaway thread based on guessing a movie]9https://www.steamgifts.com/discussion/WvWH3/guess-the-movie-gets-the-gog-key) with GoG keys, so you could do something similar.

If doesn't gain you any SG cred but the sentiment is still the same :)

People are using all kinds of threads to drop their GOG keys:
https://www.steamgifts.com/discussion/tnWVh/anti-ninjas-key-drops-no-keys-in-messages-though
https://www.steamgifts.com/discussion/MdFA5/amazon-prime-gamingfreebies-list2024-11-07-1-epic-3-gog-2-amazon
https://www.steamgifts.com/discussion/hK2kQ/orphan-keys-drop-thread
https://www.steamgifts.com/discussion/79wXh/gog-discount-codes-lets-share

or they just make their own thread and come up with something funny,

but no, making giveaways for GOG keys is not within the rules of the site.