That's a tough one. Alarm bells started ringing in my head when you stated he has been falsely accused of cheating by many previous girlfriends; and here you are, like them? There's a pattern/dynamic here that is hard to understand; it was not an "accident" that the underwear drawer was left open or is in his working desk drawer? Why not his bedroom drawer (where you probably would not snoop)? If you or I were going to keep such "trophies" I would think, at a minimum, we would keep them in a bottom drawer and you would have opened a top drawer for paper and pencil and not even thought of opening bottom desk drawers because who keeps anything "interesting" in bottom desk drawers?

So, I don't think this is going to be the only "surprise" you get in this relationship? Like I say, I don't think it was planned consciously but sounds like this guy might have a bit of unconscious stuff going on that he's picking women who tend to think he's a cheater and leaving drawers with panties in them open (ask him when you talk if he found what he was looking for in that drawer and/or if it was the last drawer he opened/closed and why didn't he leave a "different" drawer open)? Just as we have our patterns, sounds like he has some operating also that do not sound easy to deal with along with one's own?