Animations - Cycle Offset

I resolved this using a transition into itself with the transition offset properly set, and with Exit Time = 1. Also this seems as it doesn't need to have Loop Time checked, because the loop is built in the Animator Controller itself. Annoying but works

I had the same problem, and what I realized is that we were both misunderstanding what cycle offset does. It just changes where the animation starts within the loop, it won't set a point to loop back to (cutting out the beginning of the animation). I think the best solution when you have a looping animation with an intro is probably to create two separate animation clips out of it and have the first (non-looping) clip transition into the second (looping) clip in the animation controller.