Just left a relationship, but I'm falling real hard for someone in my program

Im recently out of a relationship. I feel like I shouldn't get started in a new relationship this quick out the gate, it was only a couple months ago it ended. But, I have a big fat grade school crush on someone in my program. Like giddy with butterflies and everything. I haven't felt like that in so long and I don't know what to do.

He's so smart, super talkative, is passionate about the same things as me, and cute too with really pretty eyes. I'm just feeling weird because I don't feel like he could possibly like me. I've only talked with him one time and it's not like I've ever seen him starting at me or anything, so I feel like he doesn't really like me that way and I'm way to scared to approach him directly. (Which is ridiculous, because I'm a grown adult getting a master's). I don't even know what I'd say if I did try to talk to him. It's not like this is high school and I could ask him to a party or to hang out with friends or try to be subtle, there's no reason for us to hang out other than for the sole purpose of hanging out together, and I feel like I can't approach someone I've only spoken to one time and say "go on a date with me". But maybe that's how adults do things?

I feel torn too because I just left this old relationship and I know it's probably good to give myself time alone to heal and grow. But I also don't want to not do something and miss out on this guy in case there is something there because, at least from what I know, he's got everything I could ever look for in a partner and it's incredible. I only see him in class and once it ends, I don't know if I'll see him again so I would have to take that risk. He's just everything I really like in a person and it's rare I find someone that does this kind of thing to me.