Is there an easy way to loop some audio that has a push at the start? Meaning it starts slightly before the bar

A) Make sure that you can see the Info Line in the Project Window
B) Select the audio clip you want to adjust
C) On the Info Line change the value of Snap, lower moves it earlier.

This will change it so the 1 beat in the clip and the bar line match up by sliding the clip along the timeline

You might also want to look at the Offset setting which slides the audio within the clip forwards & backwards but keeps the clip anchored to the same place in the timeline.