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!

Unreal actually also has a female protagonist.

https://unrealarchive.org/wikis/the-liandri-archives/Prisone...

Unreal gives the player their choice of protagonist. The default choice is not canonical.

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.

If Portal counts, so does Control

Control's not first-person. You are looking at Jesse's back for pretty much every moment of gameplay.