Well, you see, the g in gif stands for "graphics" which is ultimately from Greek "γραφικός," and because this is the 21st century, γ in front of a close front vowel is pronounced as neither /g/ nor /d͡ʒ/ but rather /ʝ/, which is pronounced a bit like English's y, so in its purest rendition gif is really pronounced "yiff", which doubles as homage to the online communities that OP frequents.
If you're supposed to pronounce it based on the original word instead of how the person who invented it says it, then I'd like to see giff crusaders take on everyone's terrible pronunciation of words like SCUBA (the U stands for underwater, so should be UH not EW) and NASA (the first A stands for aeronautics so should be pronounced Nair-sa).
Don't worry, I was being 100% facetious! After all, γ is generally believed to have been a hard /g/ in Ancient Greek, which is the version of Greek that "graphic" is based on and is CLEARLY the wrong way to say gif :D
Kinda sorta un-jerking (but not really) for a moment, I don't think that I'd include the rhotic in your hypothetical pronunciation in NASA and thus would say /neæ.sə/ over /neɚ.sə/. I also don't palatalize the U in SCUBA (/sku:.bə/, not /sk^(j)u:bə/), but I suspect that's just a dialectical difference.
Edit: I just saw your NZ lemmy instance name and now I understand the vowel choices. Cheers!
Just a few examples that come to mind. Additionally, the pronunciation of the individual words included in an acronym DOES NOT determine the pronunciation of that acronym. See SCUBA as an example.