How do you pronounce "Git"?
If you need to know for sure, go to the source!
Video presentation about Git by Linus Torvalds
This confirms that [gɪt] is the expected pronunciation.
The word is pronounced [ɡɪt]. This is a homophone for the verb get, which is an intentional reference to its role in retrieving a source from a repository.
It never occurred to me to even think of saying it with anything other than a hard G and a short I, so [ɡɪt].