I'm a virgin and have a small frame, but I can insert "super" tampons without trouble and the cup doesn't seem much bigger with the punch down fold... but I can't seem to insert it properly. I stick my finger in just fine, but try to do the same thing with the cup and it doesn't want to go in, or hurts a lot. I don't think lube is the issue because my hands and the cup both got quite slippery and I had trouble holding onto it -- so it kept popping open too early, often before I even made it past the labia. The feeling of suction on the vulva is... interesting, but not particularly helpful!
I tried all the folds except origami (couldn't remember how to do it but I've since checked), standing, leaning back against the wall and half-squatting, and sitting on the toilet. I usually insert tampons while sitting on the toilet and leaning back, and made the most progress that way with the cup (using the punch-down fold), but still couldn't get it in - it hurt too much or just didn't seem to want to go in at all. I live in a dorm and the bathroom has stalls, so the positions I can try are somewhat limited due to a lack of privacy.
I'm trying not to get discouraged, because I had trouble with tampons at first too, and a lot of people in this community needed some practice before it worked. I think I'm going to try again later in the shower, and try the origami fold. If it still won't work, I'll try again next period - a break may help. If I can't get the cup to work I'll probably invest in (or make) some cloth pads, since wanting to be environmentally friendly (and save money) was my main reason for wanting to use cups. (Also, even though I can insert tampons fine, they usually dry me out and hurt to remove, and I've heard the cup doesn't have that particular issue.)