AndreD1101
Welcome to the forum,
You've come to the right place for questions and answers.
But the first thing I'd like to tell you is that's not a Brown Turkey fig.
Looks more like a Negronne/VBD. Which to most ( say 95% of us ) it's better fig the the B/T.
Once the fruit get to a certain size they stop growing till about a week or so before harvest. That's when they start to swell, grow, droop and soften.
You'll know when the time come but that won't be till about late August or September. Or unless they are brebas and that will happen in about a month or so.
If you have an attached garage then you can cover them but not to an extreme.
Others with more knowledge will weigh in as well.
Congrats on your FIRST fig tree. LOL