Going through proper formal channels to get HRT tends to vary from one person to the next by quite a bit. You can check out the
Standard of Care, but be aware that they are not applied in anything like a uniform manner, when they are applied at all, which means that you may or may not be able to get on HRT within the amount of time you are talking about.
If you're certain about wanting to start HRT as soon as possible, start by
reading the terms of your insurance.

Then talk to your GP and find out what you would need to do to get a prescription -- which probably means seeing an endocrinologist. Then contact the endo and see what they require; probably a letter from a therapist. Then you can find a therapist. I'd suggest asking around local support groups from people who have experience with that endo and therapists that are known to the endo, especially ones that take your insurace (if possible). And get on it! The administrative hassle, especially with your therapist, might take longer than you think.
Anyway, that's what I would do, and more or less what I did. Good luck.