Can i begin my application even though i do not have my passport on me at this moment?

Hi i have recently lost my Australian Passport and am in the process of replacing it. I have a business trip to China planned on Jan 19-26 and was wondering how long the visa process will take?
If i get my passport early January and bring it to the centre does the visa get usually done within a week?
Alternatively can i begin the process now (i have invitation letter from China) without the passport at this moment and bring the passport and passport number when it has arrived. Would this help the process?