I'd assume it depends on where you live but here it took me a month and half for a first appointment with a GP, 3 months to go to a hospital for a fertility preservation (idk if that's the word in English) and then 2 weeks later I got my gel :3
From what I heard everyone suggests you get on the waiting list, before its usually longer then getting a therapist (usually getting into therapy takes about 6 months or longer)
Talk to Germans about this, but back in the day (10 years ago) when I started hormones America was just starting our informed consent thing and most doctors weren't on board with it yet, some people would do DIY (or even just inform that they would) then go to the doctor and say that they're already on hormones and happy with it, but would like to switch to doctor provided. It was always a risky move, but I remember hearing it worked from time to time