To update your Social Security records, you need a certified copy of your name change order from the court and a letter from your doctor saying you are transitioning. It can be from whoever is prescribing you hormones. You don't need to have completed GRS to update this.
For the passport, you need the same things. There is particular verbiage it must say, so best to look it up online. Like SSA, you don't need to have had GRS to update your gender marker with the State Department. Just a letter from the doctor prescribing you hormones saying you're transitioning. This will grant you a 2 year provisional passport. If you have a letter saying you've completed transition, you get a regular 10 year passport.
It's not a box you check on either application. You just fill them out as if you are a new person, hand them to the clerk with your documentation, and let them handle the rest.
