I have an express entry profile. Is it possible for me to apply for any of the PNPs without waiting to get an invite from them? Any advice would be much appreciated.
Yes of-course. You can and you should.
The Provincial Nomination process ends with an express entry profile. When you get a nomination letter from a province, you should create an EE profile and upload the letter there and persue the rest of the process from federal channel.
PN gives you 600 points in EE and you will get selected from EE pool at the next draw. Check this link which explains how much point you might get with a PN.