Here’s two alternative keyboard shortcut sequences:
Method 1:
Ctrl+A
J
Shift+K
Ctrl+T
Method 2:
J
Shift+K
Shift+Ctrl+K
Ctrl+T
Both methods select from time=0 to the end of the project in all tracks, and then trim to that selection.
Unfortunately there is no single operation to trim all tracks at time=0, though if you would like to suggest such a feature or some alternative way to export tracks starting at t=0, feel free to post your suggestion on this forum board: http://forum.audacityteam.org/viewforum.php?f=20