Hey mate, I was in a similar situation to you when I was young, my DP got pregnant when we'd only been going out a month.
We made it work and DD is now 16 and we're still together. However, the only reason the situation worked for us is sheer luck.
We happened to be a couple that would have likely worked out anyway. Had I had a baby with any of my prior girlfriends, it would have ended, probably even more horribly than it actually did.
The fact is, your ex girlfriend doesn't want to be in a relationship with you. You can't change that, and you shouldn't try to. Look at it from her point of view, she's just had this huge life changing experience (You have too, but not to the same extent). She needs to come to terms with that without also having to factor in a very new boyfriend.
Your focus now needs to be on your son, and being the best parent you can to him. Part of that is going to be forming a good co-parenting relationship with your ex. The best way to do that is by trying to form a successful and supportive friendship. Trying to push a relationship at this point is likely to drive her away, and will make co-parenting more difficult.