Okay, that makes more sense. I misunderstood and didn't realize you had meant gender marker change in the paragraph (that would explain it not making much sense to me).
Is NYS now accepting diagnoses in place of surgery for changing one's gender on their BC? That's news to me, last I knew they were requiring double mastectomy and a full hysterectomy (I know, not the proper, technical/medical term but we all know what it means). I'll have to look into that and see whether I might be able to get that changed sooner than anticipated..
I believe you're right that you need your birth certificate changed to change it with SS. That was how I had always understood it, that a driver's license wasn't enough. Of course, with how much it seems things may have changed since I last looked into this who knows, haha