finasteride starts working right away. it takes time for your miniturized hair follicles to become healthy enough to produce full thick hairs.
it's not like your hair would be growing great if DHT just disappeared, over time DHT has shrunk your hair follicles and some of them are now dead forever, others simply too small and thin to produce healthy hairs or even hairs at all.
so really it's not the medication that's slow to work it's your body that's slow to show any change