How much time does it take for Finasteride to show some effectiveness?

Finasteride (Propecia) takes about 6 months to have a visible effect.   It is true that Finasteride blocks the DHT receptor quickly, but the process for hair restoration is much slower.  
As DHT is blocked, the tissue in and around the hair follicle changes from a growth suppressing to a growth promoting environment.  In addition, the affected hairs (both dormant and miniaturized) need to enter into a more normal growth cycle.  All of this takes time.   
My advise would be to continue with the Finasteride (barring any side effects) for a minimum of 6 months to see what kind of impact it will have.  Right now Finasteride is one of the only medications on the market that can block the genetic reason for your male patterned hair loss - DHT.

It takes a minimum of 5-6 months to see photographic improvement using finasteride.  It's very important to take photos when you start.  Keep in mind that there are two goals: slowing down hair loss progression and improvement. About 50% of finasteride users will see more hair growth, and the earlier one starts it in their hair loss potential, the better results.  In my 20 years experience prescribing finasteride, because it slows down hair loss progression for up to 90%, the majority of my patients using it  have more hair than when they started.