Not saying I can do it now (in fact, I know I can't)...but in college I had to mount a horse up, from the ground, no girth. That's right. NONE. We got three tries.
And you know what. On my third try I did it (the first two failed attempts were due to the horse moving off as I was mounting up). I've always been a heavier rider...and the mare I was doing this on for my test out (final exam) was a round, roly poly morgan pony cross with no withers. Yet I still did it. Our teacher said that if you mount up correctly, the saddle should not move at all. He didn't want us pulling ourselves up.
Everyone in my class was able to do it within their three tries. It was kinda neat that we were able to do it.
Edit to add: we didnt ride without the girth though, it was just mount up. Sit there for a second, dismount.