Is it normal to keep trying with a guy who has a girlfriend?

I've liked this guy for a while and he recently started "dating" this girl who he has been interested in. They've never hooked up and haven't really hung out that much, they've recently just made the decision that they will start to date. In my eyes,their relationship is childish and not all that important. She has never been in a relationship and is really immature about everything that has gone on between them. I know he deserves better than that and I am convinced that it will not last between them.
The thing is, he is a great guy who is determined when he likes a girl so I'm afriad of him wasting all his time with her when she already knows that she doesn"t want it to get serious.
The reason I think that I still have a chance is because I know that he is interested in me. Maybe not as much as her, but I know that there is, or at least was, something between us. I am going to keep trying to be with him.
I don't mean that I am going to ruin their relationship but next time I see him I want to explain how I feel about everything.
Is it normal for me to keep trying when he clearly chose her over me? It feels like all the time we spent together means nothing to him, yet I know there would be potential if she was not a part of the situation.
IIN? And what do I do to make him change his mind without being a dirty manipulative boyfriend stealer?