There are some endos who recommend taking depo-provera or a different form of estrogen-blocker (typically a GnRH agonist - a more expensive route) in advance or at the same time of starting T to make the period go away first or faster.
I'm not saying that this is right for everyone or will be offered/recommended by every doctor. Depo-provera has a litany of side effects (including the fact that it doesn't always stop the bleeding), and GnRH agonists are complicated, expensive drugs too.
But if it is very important to you to get rid of your period faster, you can talk to your doctor about whether this type of route makes sense for you.