Want to drop off my daughter in a month

My daughter is going to study at a University in HK and I wanted to go drop her. I applied for the visa this week because my agency told me a month ago that I couldn't apply back then because I had to book tickets first to even apply for a leisure purpose. Although what they said turned out to be wrong, I need to get the entry permit before August 17th to join my daughter. Now they said it would take 4-6 weeks for me to get the result and that's much longer! So could you tell me if there is any way to speed up the process?