Not a "shooter", but the "No One Lives Forever" franchise is another example of a female protagonist in a first person game.
Edit: I completed forgot Chell from Portal, too!
Edit: I completed forgot Chell from Portal, too!
https://unrealarchive.org/wikis/the-liandri-archives/Prisone...
https://unreal.fandom.com/wiki/Prisoner_849
> The character of Prisoner 849 is commonly speculated to be Gina, as her model (Female 1) and skin are the first character to appear in alphabetical order; this is even reinforced by UnCreature giving the female player a bio while the male player bio just reads "See Female Player". However, the character of Prisoner 849 is completely up to the player's choice, hence the use of neutral nouns in this article.