I decided I wanted to in the first week of December last year, and started spiro mid-January and estradiol a week later. The wait was only because that was the first available appointment with the endocrinologist. I probably could have found an earlier appointment somewhere, but I figured that even though I was sure this was right, having time to mull it over was probably a good idea. More in case I decided that the timeline was wrong overall and wanted to wait, not because I thought there was any chance I'd not do it at all.
In my case, I had been in therapy in general for a couple years, but only brought up that I was trans in December, because I hadn't realized it until then. Since I'd had the feelings for so long, I wasn't concerned about it being too fast because it was obvious that it was just a matter of having taken myself seriously and realizing that I was capable of going public. My therapist had no reservations about supporting me, though I think it was a complete surprise when I told him. As it turned out, my endo required neither a letter nor any signatures to get my prescriptions. The wait of a week for the estradiol was only because I was at risk for Factor V Leiden, a heredetary clotting disorder, so I had to be tested for that to determine whether I could use pills or needed patches to start with. (Thankfully, I don't have the disorder.)