Brother, having a beard for other people is rather a shock. Why? Because they just are NOT use to it. I would rather say, buy a trimmer. First let it grow just a LITTLE bit and for a long time (1-2) months, keep it at that length. Why? So they can adapt their vision of you to their son having a beard. Then slowly make it again a bit longer..and again make them adapt to that vision of their son having a beard. It is rather a psychological games often with people. i mean the idea that they have hated a beard is even a psychological brainwashing by western media to brand somebody who has shaved off being "good, handsome, clean..etc" while it is all just nonsense from sheytan. So try to make them adapt to that picture.
In the end you will in'sha'Allah have a big beard and they will remember you like that and find it rather odd you without a beard.