Progesterone, unlike medroxyprogesterone acetate, hasn't shown to increase breast cancer risk, have negative effects on coagulation nor any androgenic effects. Mood problems also can occur more with medroxyprogesterone acetate and bio progesterone may actually improve some peoples' moods, due to its antidepressant/anxiolytic actions. It also doesn't negate estrogen's favorable cardiovascular effects.
Study after study has shown progesterone to simulate certain structures in the breast that estrogen alone cannot. It has shown to increase growth in some girls while do nothing significant in others. A paper on transsexual women concluded a progestogen is required for full breast development. It can make breasts rounder, feel fuller and can help increase nipple size. Orally, bio-availability is poor so sometimes higher doses are needed. Check with your doctor.
I see no reason to not take progesterone right away and to base it on the fact that cisgirls experience an increase in estrogen first during puberty followed by progesterone years later is not a good reason, in my opinion. We don't know why this occurs and so cannot postulate it is more favorable for breast growth. My 2 cents...
Be safe and happy your doctor prescribed you the safer and more favorable progestogen, that is IDENTICAL to what your body naturally produces.