Getting air in the lines somehow

Wont get air in m/c while pedal is depressed.
You mentioned it takes some time to get the air out.
Static test. Depress pedal, both feet as hard as you can. Basically, duplicating a hard stop. But hold it for 10-20 seconds. If there is a fluid leak you should feel pedal drop. If problem still exists, with a helper, try bleeding at master by cracking the lines. If you get air, its the master.