Are you sure you have the manifold valves lined up correctly? Also the screw in needle valve on the top of the refrigerant cans can be finicky with the self sealing cans, I had to screw it all the way down to pierce the can, but then back it off just a little to get full flow from the can, if I opened the valve all the way the can would seal itself off. Kind of silly design but whatever.
Considering the system is below atmospheric pressure and the can is pressurized, it shouldn't have any problem flowing into the system even without the compressor running at first. The compressor shouldn't kick on until there is some minimal amount of refrigerate/pressure in the system so all you have is the pressure differential to start with.
This video should help.
Only thing I'd add to this video is he showed how to purge air out of the line with the first can, but he didn't appear to repeat that process with the subsequent cans, you'll want to do that. Just make sure you've closed off the all the correct valves first otherwise you're bleeding out refrigerant that you just put into the system instead of purging air from the yellow line.